Quantum and classical statistical mechanics

We construct a self-adjoint operator on a prime-based Hilbert space whose spectral determinant matches the completed Riemann ξ-function on the critical line. This operator arises naturally within a prime-resonance framework where primes serve as fundamental eigenstates and entropy-driven stabilization enforces spectral alignment. Using a block chiral form, calibrated prime-power trace identity, and functional antiunitary symmetry, we prove that all non-trivial zeros of ζ(s) lie on ℜs = 1 2. This provides a resolution of the Riemann Hypothesis via the Hilbert-Pólya strategy, extended with resonance and entropy considerations.

The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature T can be mapped onto a fictitious system of free harmonic oscillators. To the best of our knowledge, this is the first time that such a mapping is explicitly worked out. This finding provides further theoretical support to the phenomenological harmonic oscillator models commonly used in condensed matter. Moreover, our result helps in clarifying an interpretation issue related to the presence and physical origin of the Bose-Einstein factor in the FDT.

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long-range correlations in quantum phase transitions.

Financial fraud detection faces unprecedented challenges due to increasing transaction volumes, sophisticated attack vectors, and the need for real-time processing. This paper introduces Adaptive Quantum Entanglement Networks (AQEN), a revolutionary quantum machine learning framework that leverages temporal correlations and dynamic entanglement for superior fraud detection performance. Under Assumptions 1-3 (Section 2), our theoretical analysis predicts asymptotic improvements that can scale exponentially in qubit count compared to naive classical representations for structured temporal models; empirical results validate these gains in realistic simulation regimes We establish rigorous theoretical foundations through novel mathematical frameworks, proving quantum advantage bounds for temporal fraud detection and deriving explicit performance guarantees. The core innovation lies in adaptive entanglement mechanisms that dynamically adjust quantum correlations based on transaction patterns, creating quantum representations that mirror real-world fraud network structures. Experimental validation on comprehensive financial datasets demonstrates that AQEN achieves 94.7% accuracy, 81.2% precision, and 79.8% recall, representing significant improvements over classical state-of-the-art methods (93.5% accuracy, 78.5% precision, 74.2% recall for XGBoost). Statistical analysis confirms the improvements are highly significant (p < 0.001), with AQEN achieving AUC = 0.951 compared to 0.923 for the best classical approach. The paper provides complete algorithmic specifications, quantum circuit implementations, and comprehensive performance analysis, establishing AQEN as a breakthrough approach for next-generation fraud detection systems with practical deployment potential on nearterm quantum devices.

We present empirical evidence for prime number clustering in pulsar frequencies and derive this phenomenon from first principles using standard quantum mechanics.

The analysis reveals an unexpected isomorphism between quantum eigenmodes and prime numbers, with testable predictions for resonant systems across multiple scales.

1 Empirical Observations Recent analysis of pulsar frequency data reveals statistically significant clustering around prime number ratios.

Specifically: • Millisecond pulsars show frequency peaks at 2, 3, 5, 7, 11, 13 Hz (after normalization). • Binary pulsar orbital resonances favor prime number ratios (2:3, 3:5, 5:7). • Similar prime clustering appears in atomic transition frequencies when properly scaled.

The continuum percolation of long, permeable objects is theoretically studied stressing the effect of the objects' eccentricity on the threshold percolation density and the functional form of the mean cluster size near the percolation transition. The mean cluster size, whose divergence determines the threshold density, is calculated by using a connectedness interaction-site formalism derived from the reference-interaction-site-model approximation. Our results show that the threshold density is determined by the excluded volume, and that the critical average cluster size follows an inverse power law, with the Percus-Yevick -type exponent y=2. Comparison of these results with Monte Carlo simulations, available in the literature, allows us to conclude that the formalism is able to reproduce, at least at a qualitative level, the main aspects of the percolation phenomena of these ob- jects.

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism.

This paper concerns the study of the strong stochasticity threshold (SST) in Hamiltonian systems with many degrees of freedom, and more specifically the stability problem of this threshold in the thermodynamic limit (N -+ oo). The investigation is based on a recently proposed differential geometrical description of Hamiltonian chaos. The mathematical framework is given by Eisenhart's formulation of Newtonian mechanics in a suitably enlarged configuration space-time: a Riemannian manifold equipped with an aKne metric. Using the Jacobi -Levi-Civita equation for geodesic spread, w'e estabilish a relation between curvature properties of the ambient manifold and the stabilityor instabilityof the dynamics. The use of the Eisenhart metric makes it clearly evident that a dominating source of chaoticity in Hamiltonian flows of physical interest is represented by parametric resonance induced by curvature fluctuations along the geodesics and not by negativeness of some curvature property. Here only Ricci curvature is involved because the scalar curvature vanishes identically with this metric. Thus a geometric quantity relevant to the study of chaos is the degree of bumpiness of the ambient manifold, i.e. , the integral of the Ricci curvature carried over the whole manifold with the constraint of energy constancy. This quantity, considered as a function of the energy density c, clearly marks the SST. A simple sufFicient criterion is given to identify integrable systems and is here applied to a chain of linear oscillators as well as to the Toda lattice. In the case of the Fermi-Pasta-Ulam P model we have worked out analytically the e dependence of the degree of bumpiness of the ambient manifold. This allowed us to prove that the SST is stable in the N ~oo limit. An operational definition of the critical energy density is also provided and shown to yield predictions in excellent agreement with previous results based on Lyapunov exponents.

Starting from a critical analysis of recently reported surprisingly large uncertainties in length and position measurements deduced within the framework of quantum gravity, we embark on an investigation both of the correlation structure of Planck scale fluctuations and the role the holographic hypothesis is possibly playing in this context. While we prove the logical independence of the fluctuation results and the holographic hypothesis (in contrast to some recent statements in that direction) we show that by combining these two topics one can draw quite strong and interesting conclusions about the details of the fluctuation structure and the microscopic dynamics on the Planck scale. We further argue that these findings point to a possibly new and generalized form of quantum statistical mechanics of strongly (anti)correlated systems of degrees of freedom in this fundamental regime.

The Zitter Model of the Electron interprets Zitterbewegung as a real internal motion of the electron at the speed of light, giving rise to its spin and magnetic moment. Based on this model and relying solely on four basic assumptions, we have derived numerous properties of the electron directly from its internal structure, including the de Broglie frequency, magnetic and angular momentum, Compton wavelength, the quantum magnetic flux, the quantum Hall resistance, the Lorentz factor, and the Schwinger critical field limits. By introducing a fifth assumption (a secondary helical motion), we derived the amplitude of this motion and predicted an anomalous magnetic moment with a g-factor of 1.0011607, obtained purely from geometric considerations, without any numerical fitting or free parameters.

The space of labels characterizing the elements of Schwinger’s basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character.

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes ("isothermal theorem") is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined.

The autocorrelation function for the velocity and for the electric microfield of an impurity ion in a Two Ionic Component Plasma (TICP) is considered. A simple model is constructed for this purpose that preserves the exact short time dynamics and the long time global constraint of a given self-diffusion coefficient. The memory function and then the collision effects associated with the correlation function for the self-diffusion are expressed in terms of an effective two body interaction via a screened effective potential. The basic approximation used in our approach is the “disconnected” one that refers to the collision operator. A comparison of the prediction of this model for the self-diffusion and for the autocorrelation functions with the results of the molecular dynamics simulation developed in our laboratory (PIIM) shows an acceptable agreement over a wide range of plasma coupling, impurity ion charge and concentration.

Survival is traditionally modeled as a supervised learning task, reliant on curated outcome labels and fixed covariates. This work rejects that premise. It proposes that survival is not an externally annotated target but a geometric consequence: an emergent property of the curvature and flow inherent in biological state space. We develop a theory of Self-Organizing Survival Manifolds (SOSM), in which survival-relevant dynamics arise from low-curvature geodesic flows on latent manifolds shaped by internal biological constraints. A survival energy functional based on geodesic curvature minimization is introduced and shown to induce structures where prognosis aligns with geometric flow stability. We derive discrete and continuous formulations of the objective and prove theoretical results demonstrating the emergence and convergence of survival-aligned trajectories under biologically plausible conditions. The framework draws connections to thermodynamic efficiency, entropy flow, Ricci curvature, and optimal transport, grounding survival modeling in physical law. Health, disease, aging, and death are reframed as geometric phase transitions in the manifold's structure. This theory offers a universal, label-free foundation for modeling survival as a property of form, not annotation-bridging machine learning, biophysics, and the geometry of life itself.

In the present work, a power law dissipative Carnot-like heat engine cycle of two irreversible isothermal and two irreversible adiabatic processes with finite time non-adiabatic dissipation is considered and the efficiency under two optimization criteria Ω ̇ figure of merit and efficient power, χ ep is studied. The generalized extreme bounds of the optimized efficiency under the above said optimization criteria are obtained. The lower and upper bounds of the efficiency for the low dissipation Carnot-like heat engine under these optimization criteria are obtained with the dissipation level δ = 1. In corroboration with efficiency at maximum power, this result also shows that the presence of non-adiabatic dissipation does not influence the extreme bounds on the efficiency optimized by both these target functions in the low dissipation model.

It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control [T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 090602 (2010)]. The presence of feedback control in physical systems should modify both Jarzynski equality and detailed fluctuation theorem [K. H. Kim and H. Qian, Phys. Rev. E 75, 022102 (2007)]. However, the generalized Jarzynski equality under forward feedback control has been proved by consider that the physical systems under feedback control should locally satisfies the detailed fluctuation theorem. We use the same formalism and derive the generalized detailed fluctuation theorem under nonequilibrium feedback control. It is well known that the exponential average in one direction limits the calculation of precise free energy differences. The knowledge of measurements from both directions usually gives improved results. In this aspect, the generalized detailed fluctuation theorem can be very useful in free energy calculations for system driven under nonequilibrium feedback control.

This report shows how one can find a solution to the K-SAT equations with the use of purely local computations. Such a local network, inspired by the Survey Propagation equations driven by an external input vector, potentially has an exponential number of attractors. This gives the network powerful classification properties, and permits to reconstruct either noisy or incomplete inputs. It finds applications from bayesian inference to error-correcting codes and gene-regulatory networks, and its local structure is ideal for an implementaion on FPGA. Here we write its algorithm, characterize its main properties and simulate the corresponding VHDL code. One shows that the time of convergence towards a solution optimally scales with the size of the network.

We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian Mean Field (HMF) model as a simple example. These systems generically undergo a violent relaxation to a quasi-stationary state (QSS) before relaxing towards Boltzmann equilibrium. In the collisional regime, the out-of-equilibrium one-particle distribution function (DF) is a quasistationary solution of the Vlasov equation, slowly evolving in time due to finite N effects. For subcritical energy densities, we exhibit cases where the DF is well-fitted by a Tsallis q-distribution with an index q(t) slowly decreasing in time from q ≃ 3 (semi-ellipse) to q = 1 (Boltzmann). When the index q(t) reaches an energy dependent critical value qcrit, the non-magnetized (homogeneous) phase becomes Vlasov unstable and a dynamical phase transition is triggered, leading to a magnetized (inhomogeneous) state. While Tsallis distributions play an important role in our study, we explain this dynamical phase transition by using only conventional statistical mechanics. For supercritical energy densities, we report for the first time the existence of a magnetized QSS with a very long lifetime.

We present Entropic Substrate Mechanics (ESM), a theoretical framework that grounds spacetime dynamics in topological entropy evolution. Rather than treating entropy as emergent from microscopic degrees of freedom, ESM proposes that entropy itself serves as the fundamental substrate from which both quantum mechanics and general relativity emerge. By defining a substrate entropy S = k B ln Ξ where Ξ represents the configuration space density of Planck-scale microstates through topological path integrals over spacetime foam, we derive evolution equations for an entropic curvature tensor Γ µν that governs both quantum collapse and gravitational dynamics. The theory exhibits general covariance, energy-momentum conservation, and thermodynamic consistency while making specific predictions for gravitational wave signatures, cosmic microwave background topology, and laboratory decoherence experiments. ESM introduces a fundamental distinction between substrate time τ (the intrinsic evolution parameter of the entropic substrate) and coordinate time t (the emergent temporal structure observed in physical experiments). This temporal hierarchy resolves several conceptual puzzles in quantum gravity while providing a complete computational framework for numerical investigation. The theory remains experimentally falsifiable through current and near-future observations, offering a mathematically rigorous approach to quantum gravity that maintains close connection to observational physics.

We present a unified theory of quantum measurement as an entropy-driven topological phase transition, where wavefunction collapse emerges from vortex proliferation in the presence of entropy gradients. By deriving the entropy weighting function W ∝ exp(-c|∇S| 3/2) from renormalization group flow and linking fractional dynamics to emergent spacetime viscosity, we resolve key critiques of prior models. Testable predictions include: (1) asymmetric vortex lattices in superfluid helium under thermal gradients (∇T > 300 K/m), (2) universal critical exponents (α = 1.5 ± 0.1) governing CMB spectral distortions, and (3) fractal dark matter structures (D f = 2.46±0.04). Open questions on dimensional crossover, curved-space entropy, and experimental controls frame future work.

We discuss a quantum typicality approach to examine systems composed of two subsystems at different temperatures. While dynamical quantum typicality is usually used to simulate hightemperature dynamics, we also investigate low-temperature dynamics using the method. To test our method, we investigate the energy current between subsystems at different temperatures in various paradigmatic spin-1/2 chains, specifically the XX chain, the critical transverse-field Ising chain, and the XXZ chain. We compare our numerics to existing analytical results and find a convincing agreement for the energy current in the steady state for all considered models and temperatures.

We apply the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method developed in our previous work [Smith et al., J. Chem. Phys. 142, 244112 (2015)] for the determination of the dynamic structure factor of liquid para-hydrogen and ortho-deuterium at state points of (T = 20.0 K, n = 21.24 nm(-3)) and (T = 23.0 K, n = 24.61 nm(-3)), respectively. When applied to this challenging system, it is shown that this new FK-QCW method consistently reproduces the experimental dynamic structure factor reported by Smith et al. [J. Chem. Phys. 140, 034501 (2014)] for all momentum transfers considered. This shows that FK-QCW provides a substantial improvement over the Feynman-Kleinert linearized path-integral method, in which purely classical dynamics are used. Furthermore, for small momentum transfers, it is shown that FK-QCW provides nearly the same results as ring-polymer molecular dynamics (RPMD), thus suggesting that FK-QCW provides a potentially more appealing algorithm than RPMD since it is...

We discuss a quantum typicality approach to examine systems composed of two subsystems at different temperatures. While dynamical quantum typicality is usually used to simulate high-temperature dynamics, we also investigate low-temperature dynamics using the method. To test our method, we investigate the energy current between subsystems at different temperatures in various paradigmatic spin-1/2 chains, specifically the XX chain, the critical transverse-field Ising chain, and the XXZ chain. We compare our numerics to existing analytical results and find a convincing agreement for the energy current in the steady state for all considered models and temperatures.

It is proved that under any time-periodic Hamiltonian, a nonresonant, bounded quan- tum system will reassemble itself infinitely often in the course of time. To illustrate t}mse results computer experiments are performed on both a pulsed quantum rotor and an electron in the field of periodic electromagnetic pulses.

We present a quantum dynamics method based on the propagation of interacting quan- tum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [Chem. Phys. 370 4–14 (2010)] and Schiff and Poirier [J. Chem. Phys. 136 031102 (2012)] on quantum dynamics with- out wavefunctions. It consists in determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quan- tum trajectories. The particular time-dependent propagation scheme proposed here results in very stable dynamics. Its performance is discussed by applying the method to analytical potentials in the adiabatic regime, and by combining it with the exact factorization method in the nonadiabatic regime.

The unzipping of vortex lines using magnetic-force microscopy from extended defects is studied theoretically. We study both the unzipping isolated vortex from common defects, such as columnar pins and twin-planes, and the unzipping of a vortex from a plane in the presence of other vortices. We show, using analytic and numerical methods, that the universal properties of the unzipping transition of a single vortex depend only on the dimensionality of the defect in the presence and absence of disorder. For the unzipping of a vortex from a plane populated with many vortices is shown to be very sensitive to the properties of the vortices in the two-dimensional plane. In particular such unzipping experiments can be used to measure the "Luttinger liquid parameter" of the vortices in the plane. In addition we suggest a method for measuring the line tension of the vortex directly using the experiments.

We introduce a generalized approach to one-dimensional (1D) conduction based on Haldane's concept of fractional exclusion statistics (FES) and the Landauer formulation of transport theory. We show that the 1D ballistic thermal conductance is independent of the statistics obeyed by the carriers and is governed by the universal quantum κ univ = π 2 3 k 2 B T h in the degenerate regime. By contrast, the electrical conductance of FES systems is statistics-dependent. This work unifies previous theories of electron and phonon systems and explains an interesting commonality in their behavior.

A quantum mechanical model that realizes the Z 2 × Z 2 -graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is related to parasupersymmetric quantum mechanics, though the model is not directly equivalent to either of these. The purpose of this paper is to show that novel "higher gradings" are possible in the context of non-relativistic quantum mechanics.

Amorphous magnetic solids, like metallic glasses, exhibit a novel effect: the growth of magnetic order as a function of mechanical strain under athermal conditions in the presence of a magnetic field. The magnetic moment increases in steps whenever there is a plastic event. Thus plasticity induces the magnetic ordering, acting as the effective noise driving the system towards equilibrium. We present results of atomistic simulations of this effect in a model of a magnetic amorphous solid subjected to pure shear and a magnetic field. To elucidate the dependence on external strain and magnetic field we offer a mean-field theory that provides an adequate qualitative understanding of the observed phenomenon.

The possibility of interaction among multiverses is studied assuming that in the first instants of the big-bang, many disjoint regions were created producing many independent universes (multiverses). Many of these mini-universes were unstable and they decayed, but other remained as topological remnant (like domain walls or baby universes) or possibly as mini-black-holes. In this paper, we study the quantum statistical mechanics of multiverses assuming that in the first instants of the big-bang, the relativistic symmetry was only an approximate symmetry and the interaction among multiverses was produced by non-local communication. As a warm-up, in the first part of this paper we study the statistical quantum mechanics of generally covariant systems (particles, strings and membranes) living on noncommutative spaces. In the second part, the non-local communication is implemented by noncommutativity in the fields space and the possible physical implications in cosmology are considered. As the Lorentz symmetry is broken, technically the problem is solved assuming a privileged reference frame containing the multiverses, i.e. a kind of ideal quantum gas in a reservoir. If the reservoir is very large, then one can consider a uniform multiverses distribution and approximate each multiverse as tensionless p-brane. The breaking of the relativistic symmetry induces on each multiverse a tiny harmonic interaction. The oscillation frequency for each multiverse is proportional to 1/B, where B is the noncommutativity parameter. We argue that B can identified as the primordial magnetic field, i.e. ∼ 10 -16 GeV 2 . In this model of multiverses, each multiverse interacts with other neighbour multiverses in a similar way as atoms do in the Einstein model for the specific heat of a solid. In this case, the analogous of the phonon is played by quantums with energy equal to B. Each neighbour multiverse should have a pulsation frequency Ω ∼ 10 -63 s -1 . This tiny frequency could suggest that the relativistics invariance -from the cosmological point of view-is almost exact and the multiverses could be not detected using the presently astronomical observations.

In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting neurons indexed by a lattice d . The neurons are subject to noise, which is modelled as a correlated martingale. The probability law governing the noise is strictly stationary, and we are therefore able to find a LDP for the probability laws Π n governing the stationary empirical measure μn generated by the neurons in a cube of length (2n + 1). We use this LDP to determine an LDP for the neural network model. The connection weights between the neurons evolve according to a learning rule / neuronal plasticity, and these results are adaptable to a large variety of neural network models. This LDP is of great use in the mathematical modelling of neural networks, because it allows a quantification of the likelihood of the system deviating from its limit, and also a determination of which direction the system is likely to deviate. The work is also of interest because there are nontrivial correlations between the neurons even in the asymptotic limit, thereby presenting itself as a generalisation of traditional mean-field models.

A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytic expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected, which is consistent with Gaussian tails of velocity distributions. A dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail.

The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in classical and quantum case.

We want to understand whether and to what extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e., not purposefully designed) engine-bath interactions, the workoptimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is Levinthal's paradox in the protein folding problem. The resolution of this paradox for realistic proteins allows to construct engines that can extract at a finite power 40% of the maximally possible work reaching 90% of the maximal efficiency. For purposefully designed engine-bath interactions, the Carnot efficiency is achievable at a large power.

A novel approach is proposed, termed Partial-Coupled Mode Space (PCMS), for simulation of quantum transport in nanoscale devices. The PCMS integrates advantage of Coupled Mode Space (CMS) in accuracy and Uncoupled Mode Space (UMS) in reduction of computational burden. Partial coupling between the modes of the nanoscale device is achieved by coupling the odd-modes and even-modes separately. N-type FinFETs were simulated by the proposed approach and compared with the fully CMS accuracy and simulation time. The simulation was carried out on set of devices that satisfy the requirements of the International Technology Roadmap for Semiconductors (ITRS). The simulations show that our PCMS saves more than 65 % of the computational time with error less than 0.1 % and 0.01 % in the device charge and terminal current respectively compared to the CMS.

We present a constructive proof of the Riemann Hypothesis based on the Hilbert-Pólya conjecture. By identifying a self-adjoint operator H, whose spectrum corresponds to the imaginary parts of the nontrivial zeros of the analytically continued Riemann zeta function ζ(s), we demonstrate that all nontrivial zeros lie on the critical line Re(s) = 1 2. The operator is realized through the framework of noncommutative geometry, utilizing the spectral triple (A, H, D) and the thermodynamical time flow on the adele class space. This approach aligns with Alain Connes' construction and provides a spectral interpretation consistent with both known numerical results and analytical properties of ζ(s). The proof concludes with a contradiction argument based on the functional equation and zero distribution statistics.

For a composition I whose first part exceeds 1, we can define the multiple t-value t(I) as the sum of all the terms in the series for the multiple zeta value ζ(I) whose denominators are odd. In this paper we show that if I is composition of n ≥ 3, then t(I) = (-1) n-1 t( Ī) mod products, where Ī is the reverse of I, and both sides are suitably regularized when I ends in 1. This result is not true for multiple zeta values, though there is an argument-reversal result that does hold for them (and for multiple t-values as well). We actually prove a more general version of this result, and then use it to establish explicit formulas for several classes of multiple t-values and interpolated multiple t-values.

This paper is written in the spirit of the Langlands Program-a profound framework in modern mathematics that seeks unity across disparate domains such as number theory, geometry, and representation theory. While the present work does not employ the formal machinery of Langlands theory, such as automorphic forms or L-functions in their standard analytic context, it is driven by a similar philosophical motivation: to uncover structural harmony where algebraic symmetries, geometric alignments, and infinitesimal analytic behavior coalesce. Here, the Riemann Hypothesis is reimagined not merely as a conjecture about the real parts of the zeta function's nontrivial zeros, but as a geometric-algebraic equilibrium condition: a balance between infinitesimal deviations (captured via hyperreal extensions), perspectival coherence (modeled through projective geometry), and local field-theoretic symmetries (expressed through Galois-like group actions). This triadic synthesis aligns naturally with the Langlands ideal-that global mathematical truths emerge from the coordination of local structural phenomena.

When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added ‘by hand’. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node ‘quantum wire’ connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects ...

The Bose-Einstein energy spectrum of a quantum gas, confined in a rigid cubic box, is shown to become discrete and strongly dependent on the box geometry (size L), temperature, T and atomic mass number, A at , in the region of small y=A at TV lB . This behavior is the consequence of the random state degeneracy in the box. Furthermore, we demonstrate that the total energy does not obey the conventional law any longer, but a new law, which depends on y and on the quantum gas fugacity. This energy law imposes a faster decrease to zero than it is classically expected, for y -> 0. The lighter the gas atoms, the higher the temperatures or the box size, for the same effects in the discrete Bose-Einstein regime.

The effect of quantum fluctuations on a nearly flat, nonrelativistic twodimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to stiffen the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

The working paper "The Duality of Yin-Yang in Quantum Mechanics: A Philosophical and Scientific Analysis" explores how the ancient Chinese philosophy of Yin-Yang connects with modern physics, especially quantum mechanics. It highlights philosophical parallels, such as wave-particle duality and matter-antimatter relationships, which mirror Yin-Yang's concept of interdependent opposites. Visually, recent experiments showing entangled photons resembling the Yin-Yang symbol suggest a symbolic link. Theoretically, frameworks like complex-valued mechanics propose that quantum phenomena could be understood through Yin-Yang principles, though these ideas are still developing. The paper also notes historical influences, like Niels Bohr's use of the Yin-Yang symbol, but acknowledges that these connections are mostly philosophical, with debates about their scientific validity. It calls for further research to bridge Eastern and Western thought.

In this paper, we study the Feingold-Peres model as an example, which is a well-known paradigm of quantum chaos. Using semiclassical analysis and numerical simulations, we study the statistical properties of observables in few-body systems with chaotic classical limits and the emergence of random matrix theory universality. More specifically, we focus on: 1) the applicability of the eigenstate thermalization hypothesis in few-body systems and the dependence of its form on the effective Planck constant and 2) the existence of a universal random matrix theory description of observables when truncated to a small microcanonical energy window. Our results provide new insights into the established field of few-body quantum chaos and help bridge it to modern perspectives, such as the general eigenstate thermalization hypothesis (ETH).