Berry phase

I present supporting simulations that demonstrate how vibrational dynamics can reproduce behaviors typically attributed to particle-based quantum systems. A phase-difference model shows that stable equilibria generate robust effective charge. A two-level vibrational system exhibits Rabi oscillations, confirming discrete transitions under resonant driving. Coupled oscillators synchronize their phases, paralleling multi-body stability in atomic and molecular systems. Together, these results confirm that charge, energy quantization, and many-body coherence can emerge from resonance in the Dynamic Matter field, providing strong support for Vibrational Theory.

The reconciliation of quantum mechanics and general relativity remains one of the most profound challenges in modern physics. This paper introduces the Geometric-Polarimetric Duality Theorem, a novel theoretical framework that extends the standard treatment of photon polarization under gravitational lensing by incorporating quantum geometric phases. The theorem posits that the unitary transformation acting on a photon's polarization state along a null geodesic in curved spacetime decomposes uniquely into a path-dependent dynamic phase operator and a homotopy-invariant geometric phase operator, the latter manifesting as a topological phase akin to the Berry phase but generalized to gravitational fields. Derived from the holonomy of the local Lorentz connection reduced to the photon's little group, this duality provides a rigorous synthesis of gauge theory, differential geometry, and quantum information principles. Building on established literature, such as studies on polarization rotation in gravitational lensing and geometric phases for photons in general relativity, the theorem addresses gaps in current models that overlook non-Abelian effects and topological contributions. Through mathematical derivations and numerical simulations of parallel transport in Schwarzschild spacetime, we demonstrate the theorem's validity and extract measurable signatures, including a geometric phase shift of approximately 0.209 radians for photons with impact parameter b = 5.5M. These results have profound implications for cosmology, enabling enhanced delensing of cosmic microwave background (CMB) B-modes, precision probes of spacetime curvature in lensed quasars, and novel tests of quantum gravity phenomenology. Applications extend to entangled photon pairs, where the shared geometric phase could modulate entanglement, offering a pathway to detect low-frequency gravitational waves via quantum interferometry. This work not only elevates gravitational lensing from a classical correction to a quantumgeometric tool but also opens the field of quantum cosmography, potentially resolving degeneracies in cosmological parameters and providing ultra-precise measurements of the Riemann tensor over cosmic scales. Future experimental verification with observatories like the Event Horizon Telescope or CMB-S4 could confirm these predictions, bridging the quantum-classical divide in gravitational physics.

The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity λ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to λ. The position operator generates translations in momentum space. We show that a ray-representation for these translations emerges due to the non-commuting components of the position operators and relate this to the Berry-phase for photons. The Tomita-Chiao experiment then gives support for this relativistic and quantum mechanical description of photons in terms of non-commuting position operators.

abhors singularities. “So should we, ” responds the physicist. However, the epistemic assessments of Batterman concerning the matter prove to be less clear, for in the same vein he write that singularities play an essential role in certain classes of physical theories referring to certain types of critical phenomena. I devise a procedure (“methodological fundamentalism”) which exhibits how singularities, at least in principle, may be avoided within the same classes of formalisms discussed by Batterman. I show that we need not accept some divergence between explanation and reduction (Batterman 2002), or between epistemological and ontological fundamentalism (Batterman 2004, 2005). Though I remain sympathetic to the ‘principle of charity ’ (Frisch (2005)), which appears to favor a pluralist outlook, I nevertheless call into question some of the forms such pluralist implications take in Robert Batterman’s conclusions. It is difficult to reconcile some of the pluralist assessments that ...

A Landau-Zener multi-crossing method has been used to investigate the tunnel splittings in high quality Mn12-acetate single crystals in the pure quantum relaxation regime and for fields applied parallel to the magnetic easy axis. With this method several individual tunneling resonances have been studied over a broad range of time scales. The relaxation is found to be non-exponential and a distribution of tunnel splittings is inferred from the data. The distributions suggest that the inhomogeneity in the tunneling rates is due to disorder that produces a non-zero mean value of the average transverse anisotropy, such as in a solvent disorder model. Further, the effect of intermolecular dipolar interaction on the magnetic relaxation has been studied.

We address the subject of transport in one-dimensional ballistic polygon loops subject to Rashba spin-orbit coupling. We identify the role played by the polygon vertices in the accumulation of spinrelated phases by studying interference effects as a function of the spin-orbit coupling strength. We find that the vertices act as strong spin-scattering centers that hinder the developing of Aharovov-Casher and Berry phases. In particular, we show that the oscillation frequency of interference pattern can be doubled by modifying the shape of the loop from a square to a circle.

Modern physics faces unresolved questions such as the unification of gravity with
quantum mechanics and the origin of fundamental particle masses. TUOMGN
offers a novel paradigm, postulating that the universe is a single, vast, and timeless
granular medium where all observed phenomena are emergent properties. This
paper provides a complete overview of TUOMGN, structured to demonstrate its
self-consistency and predictive power.

A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change ΔF of a system at inverse temperature β from an ensemble average of nonequilibrium exponential work, i.e., 〈e^{-βW}〉=e^{-βΔF}. The number of experimental work values needed to reach a given accuracy of ΔF is determined by the variance of e^{-βW}, denoted var(e^{-βW}). We discover in this work that var(e^{-βW}) in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging var(e^{-βW}) at sufficiently low temperatures, markedly different from the classical behavior. The divergence of var(e^{-βW}) indicate...

In this paper we suggested a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the Schrödinger equation is obtained. The wave function is shown to be the eigenfunction of the Sturm-Liouville problem in which we expand virtual photon to include it implicitly into consideration. It is shown that the non-locality of quantum mechanics is related only with virtual photon. As an example, the zero-energy of harmonic oscillator is obtained from classical equations.

The two apparently disparate phenomena, viz. the Klein tunneling and the electric field driven topological phase transition(TPT), exhibited by the silicene converge on the issue of the no change in the pseudo-spin. An ensuing possibility is that the former, in the case of a normal-magnetic-normal silicene junction, may be considered theoretically as a probe to ascertain the onset of the latter. In this communication, we explore this option and calculate the total transmission probability(TTP). We find that TPT is characterized by a cusp in a plot of TTP as a function of the electric field.

To take full advantage of the well-developed field-theoretic methods, Magnonics needs a yet-existing Lagrangian formulation. Here, we show that Landau-Lifshitz magnetodynamics is a member of the covariant-Schrödinger-equation family of Hamilton models and apply the covariant background method arriving at the Ginzburg-Landau Lagrangian formalism for magnons in an instanton background. Magnons appear to be nonrelativistic spinless bosons, which feel instantons as a gauge field and as a Bose condensate. Among the examples of the usefulness of the proposition is the recognition of the instanton-induced phase shifts in magnons as the Berry phase and the interpretation of the spin-transfer-torque generation as a ferromagnetic counterpart of the Josephson supercurrent.

We present a novel setup that allows the observation of the geometric phase that accompanies polarization changes in monochromatic light beams for which the initial and final states are different (so-called non-cyclic changes). This Pancharatnam-Berry phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches.

We propose a non-algorithmic quantum computation model based on phase resonance, dynamic plasma coupling, and energy-driven convergence. Unlike gate-based or adiabatic quantum computing, this model computes via transition into stable energetic configurations defined by resonance conditions. We present a normalized Hamiltonian formalism, identify stability criteria, define Lindblad dissipation, and demonstrate a prototype numerical convergence scenario.

We propose a non-algorithmic quantum computation model based on phase resonance, dynamic plasma coupling, and energy-driven convergence. Unlike gate-based or adiabatic quantum computing, this model computes via transition into stable energetic configurations defined by resonance conditions. We present a normalized Hamiltonian formalism, identify stability criteria, define Lindblad dissipation, and demonstrate a prototype numerical convergence scenario.

The quantum scaling behavior of deconfined spinons for a class of field theoretic models of quantum antiferromagnets is considered. The competition between the hedgehogs and the Berry phases is discussed from a renormalization group perspective. An important result following from our analysis is the computation of the anomalous dimension for the decay of spin correlations. Our results confirm the expectation that the transition from a Néel to a valence-bond solid state belongs to a completely new universality class.

Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry phase term that projects out the S = 1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.

We derive a gauge-invariant low-energy effective model of the SU(2) Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type, irrespective of the gauge choice. In the maximally Abelian gauge, especially, we demonstrate that the model exhibits both quark confinement and gluon confinement: the Wilson loop average has area law and the Schwinger function violates reflection positivity. Moreover, we give a formula for the string tension calculable from the gluon propagator of the gauge-invariant field strength and gives a good estimate for the string tension. We discuss if quark confinement and gluon confinement are of the same origin attributed to the gluon propagator in the deep infrared momentum region.

We have constructed general dimensional hyperdiamond lattices which are analogues of the three dimensional diamond lattice. Each site has the minimal number of bonds as possible in that dimension and the structure of the bond vectors is similar to that of the Clifford algebra. Furthermore, the spectrum zeros of the tight-binding hopping model on the hyperdiamond lattice are also investigated. The number of zeros is larger than two except for the two dimensional lattice, so that the minimal-doubling action cannot be realized on these lattices.

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson and baryon structures, the mass-gap problem, zitterbewgung, Berry phase, renormalization, and related issues.

A theoretical model of transmission and reflection of an electron with spin is proposed for a mesoscopic ring with rotating localized magnetic moment. This model may be realized in a pair of domain walls connecting two ferromagnetic domains with opposite magnetization. If the localized magnetic moment and the traveling spin is ferromagnetically coupled and if the localized moment rotates with opposite chirality in the double-path, our system is formulated in the model of an emergent spin-orbit interaction in a ring. The scattering problem for the transmission spectrum of the traveling spin is solved both in a single path and a double path model. In the double path, the quantum-path interference changes dramatically the transmission spectrum due to the effect of the Berry phase. Specifically, the spin-flip transmission and reflection are both strictly forbidden.

We measure electron localization in different materials by means of a "localization tensor", based on Berry phases and related quantities. We analyze its properties, and we actually compute such tensor from first principles for several tetrahedrally coordinated semiconductors. We discuss the trends in our calculated quantity, and we relate our findings to recent work by other authors. We also address the "hermaphrodite orbitals", which are localized (Wannier-like) in a given direction, and delocalized (Bloch-like) in the two orthogonal directions: our tensor is related to the optimal localization of these orbitals. We also prove numerically that the decay of the optimally localized hermaphrodite orbitals is exponential.

We propose a novel framework to describe geometric phases in quantum systems under non-adiabatic conditions by introducing the concept of a hidden geometric phase. Conventional geometric phases, such as the Berry phase, rely on adiabatic evolution, limiting their applicability in rapidly changing systems. Here, we remove this constraint by reinterpreting the geometric phase as arising from a dynamically evolving reference basis, independent of the external topological features. The hidden phase is revealed through transitionless quantum control techniques, ensuring pure geometric phase accumulation even in non-adiabatic regimes. Our method offers an exact solution to the neutron spin rotation phase in the Bitter-Dubbers experiment, aligning more closely with experimental data without depending on adiabatic approximations. This unexpected result broadens our understanding of the geometric phase observed in neutron spin rotation beyond the adiabatic conditions that are conventionally required.

We propose a novel framework to describe geometric phases in quantum systems under non-adiabatic conditions by introducing the concept of a hidden geometric phase. Conventional geometric phases, such as the Berry phase, rely on adiabatic evolution, limiting their applicability in rapidly changing systems. Here, we remove this constraint by reinterpreting the geometric phase as arising from a dynamically evolving reference basis, independent of the external topological features. The hidden phase is revealed through transitionless quantum control techniques, ensuring pure geometric phase accumulation even in non-adiabatic regimes. Our method offers an exact solution to the neutron spin rotation phase in the Bitter-Dubbers experiment, aligning more closely with experimental data without depending on adiabatic approximations. This unexpected result broadens our understanding of the geometric phase observed in neutron spin rotation beyond the adiabatic conditions that are conventionally required.

It is shown that standard computations of electronic structures of polyatomic systems that yield the global minimum configuration and vibrational frequencies may be faulty if the symmetry of this configuration is lower than the highest possible one and the origin of this distortion, which is always due to the Jahn-Teller effect, is neglected; this may lead, in particular, to the loss of the Berry phase factor that changes the vibronic energy level spectrum and which we show to be present even when there are no apparent conical intersections. The general case and the ozone molecule are analyzed.

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if N is large enough. We argue that nonperturbatively this result should persist down to N = 2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent η for the decay of the two-spin correlation function to first-order in ǫ = 4 -d. We also note the scaling relation η = d + 2(1 -ϕ/ν) connecting the exponent η for the decay to the correlation length exponent ν and the crossover exponent ϕ.

We apply a general method developed recently for the derivation of the diagonal representation of an arbitrary matrix valued quantum Hamiltonian to the particular case of Bloch electrons in an external electromagnetic field. We find the diagonal representation as a series expansion to the second order in . This result is the basis for the determination of the effective in-band Hamiltonian of interacting Bloch electrons living in different energy bands. Indeed, the description of effects such as magnetic moment-moment interactions mediated by the magnetic part of the full electromagnetic interaction requires a computation to second order in . It is found that the electronic current is made of two contributions: the first one comes from the velocity and the second one is a magnetic moment current similar to the spin current for Dirac particles. This last contribution is responsible for the interaction between magnetic moments similarly to the spin-spin interaction in the Breit Hamiltonian for Dirac electrons in interaction.

It has been recently found that the equations of motion of several semiclassical systems must take into account anomalous velocity terms arising from Berry phase contributions. Those terms are for instance responsible for the spin Hall effect in semiconductors or the gravitational birefringence of photons propagating in a static gravitational field. Intensive ongoing research on this subject seems to indicate that actually a broad class of quantum systems might have their dynamics affected by Berry phase terms. In this article we review the implication of a new diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of . In this approach both the diagonal energy operator and dynamical operators which depend on Berry phase terms and thus form a noncommutative algebra, can be expanded in power series in . Focusing on the semiclassical approximation, we will see that a large class of quantum systems, ranging from relativistic Dirac particles in strong external fields to Bloch electrons in solids have their dynamics radically modified by Berry terms.

We propose a novel protocol for the creation of macroscopic quantum superposition (MQS) states based on a measurement of a non-monotonous function of a quantum collective variable. The main advantage of this protocol is that it does not require switching on and off nonlinear interactions in the system. We predict this protocol to allow the creation of multiatom MQS by measuring the number of atoms coherently outcoupled from a two-component (spinor) Bose-Einstein condensate.

How to explain the Aharonov-Bohm (AB) effect remains deeply controversial, particularly regarding the tension between locality and gauge invariance. Recently Wallace argued that the AB effect can be explained in a local and gauge-invariant way by using the unitary gauge. In this paper, I present a critical analysis of Wallace's intriguing argument. First, I show that the unitary gauge transforms the Schrödinger equation into the Madelung equations, which are expressed entirely in terms of local and gauge-invariant quantities. Next, I point out that an additional quantization condition needs to be imposed in order that the Madelung equations are equivalent to the Schrödinger equation, while the quantization condition is inherently nonlocal. Finally, I argue that the Madelung equations with the quantization condition can hardly explain the the AB effect, even if in a nonlocal way. This analysis suggests that the unitary gauge does not resolve the tension between locality and gauge invariance in explaining the AB effect, but highlights again the profound conceptual challenges in reconciling the AB effect with a local and gauge-invariant framework.

We investigate a non-Hermitian Aubry-André-Harper model with short-range as well as long-range p-wave pairing. Here, the non-Hermiticity is introduced through the on-site potential. A comprehensive analysis of this system's critical aspects, like eigenspectra, topological properties, localization properties, and the transition from real to complex energies, is conducted. Specifically, we observe the emergence of Majorana zero modes in the case of short-range pairing, whereas the massive Dirac modes emerge in the case of long-range pairing. More importantly, for both cases of pairing, we observe double-phase transitions, that is, simultaneous transitions of topological phases and multifractal to localized phases. Additionally, again, for both the ranges of pairing, we identify another double-phase transition, where delocalized (or metallic) to a critical multifractal state transition is accompanied by an unconventional shift from real to complex energies. Unlike the short-range pairing case, we observe mobility edges in the case of the long-range pairing.

We formulate analytically the reflection of a one dimensional, expanding free wave-packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule and a classical object. We derive a threshold criterion for the values of the dynamic parameters so that reciprocal (Kramers-Kronig) relations hold in the time domain between the log-modulus of the wp and the (analytic part of its) phase acquired during the reflection. For an electron, in a typical case, the relations are shown to be satisfied. For a molecule the modulus-phase relations take a more complicated form, including the so called Blaschke term. For a classical particle characterized by a large mean momentum (hK >> h trajectory length (size of wave-packet) 2 >>>

It is one of the challenges of modern physics to describe the effect of the (macroscopic) environment on the evolution of a quantum system. Its roots are in the perennial problem of the incompatibility of irreversible processes with the time-reversal symmetry of the system. The Lindblad equation approach is one of the ways to account for the environment-system interaction in a consistent form. In a subsequent development the ''square-root method'', originally devised by B. Reznik (Phys. Rev. Lett. 76 (1996) 1192), was used for the reduced density matrix evolution under effect of the Lindblad operators (A. Yahalom and R. Englman, Physica A 371 (2006) 368). In this formulation the nm element of the time (t) dependent density matrix is written in the form q nm ðtÞ ¼ 1 A P A a¼1 c a n ðtÞc aà m ðtÞ. The so called ''square root factors'', the c(t)'s, are non-square matrices and are averaged over A systems (a) of the ensemble. This square-root description is exact. The method is here applied to incorporate Lindblad-type processes into the evolution of a degenerate quantum system. Specifically, the effect of a dissipative environment on the topological or Berry phase (BP) is here studied for a system consisting of a spin-doubly degenerate orbital (E), belonging to the cubic G3 2 or C 8 representation, subject to time-periodically varying stress and magnetic fields. The environmental effects redistribute the component amplitude of the initial wave packet and, with a general precessional motion of the magnetic field, change the BP markedly. The changes in the BP are suppressed for the magnetic field precessing on a large circle, in accordance with previous results (D.M. Tong et al., Phys. Rev. Lett. 93 (2004) 080405).

A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow. When the stationary Born-Oppenheimer description for nearly degenerate state is regarded as "embedded" in a broader dynamic formulation, namely through solution of the time dependent Schrödinger equation, the wave function becomes necessarily complex. The analytic behavior of this function in the complex time-plane can be exploited to gain information about the connection between phases and moduli of the componentamplitudes. One form of this connection are a pair of reciprocal (Kramers-Kronig type) relations in the complex time-domain. These show that certain phase changes in a component amplitude (such as, e.g., lead to a non-zero Berry-phase) require changes in the amplitude-moduli, too, and imply degeneracies of the electronic state. The subject of conical degeneracy, or intersection, of adjacent potential surface is extended to nonlinear nuclear-electronic coupling, which can then result in multiple conical degeneracies on a nuclear coordinate plane. We treat cases of double and fourfold intersections, the latter under trigonal symmetry, and employ an analytic-graphical phase tracing method to obtain the resulting Berry phases as the system circles around some or all of the degeneracy points. These phases can take up values that are all integral multiples of π, with integers that vary with the physical situation (or with the model postulated for it). A further type of invariance, with respect to gauge transformation, is also tied to the complex form of the wave function. For a many-component state this leads to a consideration of tensorial (Yang-Mills type) fields F for molecular systems. It is shown that it is the truncation of the Born-Oppenheimer electron-nuclear superposition that generates the molecular Yang-Mills fields. The equations of motion for the nuclear degrees of freedom are derived from a Lagrangean density L, representing a non-Abelian situation. In L the non-adiabatic coupling terms (NACTs), that express the electronic background on the nuclear states, enter as vector potentials (or gauge fields). We demonstrate a deep lying interrelation between two apparently distinct theoretical developments: that which led to the discovery of the Yang-Mills fields from considerations of local gauge-invariance, and the use of an adiabatic-diabatic transformation matrix for the molecular case due to Baer. A generalized form of the NACTs is found, such that it makes the field F vanish for a complete electronic set. Lastly, the use of phases and moduli as variables was found to be very convenient to obtain variationally the equation of continuity and the Hamilton-Jacobi equations from the Lagrangian of an electron following either the Schrödinger or the Dirac equation. In the latter case, to a good approximation (in the nearly non-relativistic limit) the phases in the different spinor components are not scrambled together and their Berry phases are unaffected.

We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a n-fold degenerate eigenspace of a family of Hamiltonians parametrized by a manifold M. The point of M represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops in the control M induce non trivial unitary transformations on the computational space. For a generic system it is shown that this mechanism allows for universal quantum computation by composing a generic pair of loops in M.

The problem of degeneracies, descending from the Born-Oppenheimer (B-O) approximation serves as a "comeback backdoor" of the principle of complementarity, but on a much more subtle level. Quantum mechanics incorporates both mechanical and field theory features, which results in the well-known particlewave aspects of complementarity. The degeneracy problem, however, prompts a new type of "property-object" complementary phenomena. This leads to serious consequences: Field theoretical methods, unlike mechanical ones, are incapable of separating the internal and the external degrees of freedom with respect to the centre of gravity, but on the other hand adapt relativistically in a natural manner very similar to the space-time formulas of Maxwell's equations. The solutions of the quantum field equations, relativistic in the mentioned specific sense, yield singularities at symmetric points that correspond to the well-known B-O degeneracies giving the latter in actual fact a metaphysical attribute. However, Nature has in this case a more sophisticated method or modus operandi to avoid degenerations and to instigate symmetry violations.

In a recent preprint (cond-mat/9803170), van Langen, Knops, Paasschens and Beenakker attempt to re-analyze the proposal of Loss, Schoeller and Goldbart (LSG) [Phys. Rev. B 48, 15218 (1993)] concerning Berry phase effects in the magnetoconductance of diffusive systems. Van Langen et al. claim that the adiabatic approximation for the Cooperon previously derived by LSG is not valid in the adiabatic regime identified by LSG. It is shown that the claim of van Langen et al.

The layered transition-metal dichalcogenide PdTe2 has been discovered to possess bulk Dirac points as well as topological surface states. By measuring the magnetization (up to 7 T) and magnetic torque (up to 35 T) in single crystalline PdTe2, we observe distinct de Haas–van Alphen (dHvA) oscillations. Eight frequencies are identified with H||c, with two low frequencies (F α = 8 T and F β = 117 T) dominating the spectrum. The effective masses obtained by fitting the Lifshitz–Kosevich (LK) equation to the data are m α * = 0.059 m 0 and m β * = 0.067 m 0 where m 0 is the free electron mass. The corresponding Landau fan diagrams allow the determination of the Berry phase for these oscillations resulting in values of ∼0.67π for the 3D α band (hole-type) (down to the 1st Landau level) and ∼0.23π–0.73π for the 3D β band (electron-type) (down to the 3rd Landau level). By investigating the angular dependence of the dHvA oscillations, we find that the frequencies and the corresponding Berry p...

In this paper, a 3 × 3-matrix representation of Birman-Wenzl-Murakami(BWM) algebra has been presented. Based on which, unitary matrices A(θ, ϕ1, ϕ2) and B(θ, ϕ1, ϕ2) are generated via Yang-Baxterization approach. A Hamiltonian is constructed from the unitary B(θ, ϕ) matrix. Then we study Berry phase of the Yang-Baxter system, and obtain the relationship between topological parameter and Berry phase.

In this paper, a 3 × 3-matrix representation of Birman-Wenzl-Murakami(BWM) algebra has been presented. Based on which, unitary matrices A(θ, ϕ1, ϕ2) and B(θ, ϕ1, ϕ2) are generated via Yang-Baxterization approach. A Hamiltonian is constructed from the unitary B(θ, ϕ) matrix. Then we study Berry phase of the Yang-Baxter system, and obtain the relationship between topological parameter and Berry phase.

We investigate the Berry phase of a spin system in a q-deformed magnetic field. The Berry phase depends on parameter q and which causes the deformation of the Berry phase. When q = 1, the parameter space for the spin-half particles in magnetic field is deformed and immovable at the point of ϕ = 0, π/2, π. The same Hamiltonian can also be constructed by q-deformed Lie-algebra and magnetic field.

We study the effect of a Chern-Simons (CS) term in the phase structure of two different Abelian gauge theories. For the compact Maxwell-Chern-Simons theory, with the CSterm properly defined, we obtain that for values g = n/2π of the CS coupling with n = ±1, ±2, the theory is equivalent to a gas of closed loops with contact interaction, exhibiting a phase transition in the 3dXY universality class. We also employ Monte Carlo simulations to study the noncompact U (1) Abelian Higgs model with a CS term. Finite size scaling of the third moment of the action yields critical exponents α and ν that vary continuously with the strength of the CS term, and a comparison with available analytical results is made.

The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band is equal to π × (odd integer) and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than ln 2 (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss this lower bound is related to vanishing of the expectation value of a certain non-local operator which creates a kink in 1D systems.

This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but have not attracted much attention, to express the resolvent of the GPI Hamiltonian as well as its spectral and scattering properties. It is also shown that the GPI yields one of the simplest models in which a non-trivial Berry phase is exhibited. Furthermore, the generalized Kronig-Penney model corresponding to the GPI is discussed. We show that there are three different types of the high-energy behaviour for the corresponding band spectrum.

We propose a novel spin-optronic device based on the interference of polaritonic waves traveling in opposite directions and gaining topological Berry phase. It is governed by the ratio of the TE-TM and Zeeman splittings, which can be used to control the output intensity. Due to the peculiar orientation of the TE-TM effective magnetic field for polaritons, there is no analogue of the Aharonov-Casher phaseshift existing for electrons.

In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex

We suggest a theoretical model to characterize stability and chaotic behaviour for a dynamical system consisting of two ions confined in a three dimensional (3D) Paul trap, depending on two control parameters: the axial angular moment and the ratio between the radial and axial trap frequencies. When the electric potential is time independent or in case the pseudopotential approximation for radiofrequency (RF traps) is valid, an autonomous Hamilton function can be associated to the ion system. In such case, the family of electric potentials can be characterized according to the Morse theory, the bifurcation theory, and the catastrophe theory. This classification qualitatively determines the structure of the phase space, the minimum, maximum, and critical points, the periodic orbits and the separatrices. Besides the case of axial motion, ion dynamics in a nonlinear trap is generally non-integrable and chaotic orbits prevail in the phase portrait, except specific neighborhoods around t...

Nonrelativistic electrons hopping on the honeycomb lattice of graphene emerge as massless Dirac fermions. When the on-site repulsion between electrons on a honeycomb lattice exceeds a critical value, as it is the case for the dehydrated precursor of the high-temperature superconductor Na 2 CoO 2 × yH 2 O, the system spontaneously breaks its SU(2) s spin symmetry and becomes an antiferromagnet. The emergence of antiferromagnetism is analogous to the spontaneous breakdown of the SU(2) L × SU(2) R chiral symmetry in QCD. Just as the low-energy physics of pions and nucleons is described by baryon chiral perturbation theory, magnons and holes in an antiferromagnet are also described by a systematic low-energy effective theory. Both the chiral condensate in QCD and the staggered magnetization in an antiferromagnet act as a quantum mechanical rotor when the theory is put in a finite volume. When a nucleon is propagating through the QCD vacuum or when a hole is doped into an antiferromagnet, a Berry phase arises from a geometric monopole gauge field and the angular momentum of the rotor is quantized in half-integer units. The finite-size effects of the rotor spectrum depend on the low-energy parameters of the corresponding effective theories.