Statistical Mechanics
New submissions
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New submissions for Fri, 17 May 24
- [1] arXiv:2405.09642 [pdf, other]
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Title: LeaPP: Learning Pathways to Polymorphs through machine learning analysis of atomic trajectoriesComments: 26 pages, 20 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech)
Understanding the mechanisms underlying crystal formation is crucial. For most systems, crystallization typically goes through a nucleation process that involves dynamics that happen at short time and length scales. Due to this, molecular dynamics serves as a powerful tool to study this phenomenon. Existing approaches to study the mechanism often focus analysis on static snapshots of the global configuration, potentially overlooking subtle local fluctuations and history of the atoms involved in the formation of solid nuclei. To address this limitation, we propose a methodology that categorizes nucleation pathways into reactive pathways based on the time evolution of constituent atoms. Our approach effectively captures the diverse structural pathways explored by crystallizing Lennard-Jones-like particles and solidifying Ni$_3$Al, providing a more nuanced understanding of nucleating pathways. Moreover, our methodology enables the prediction of the resulting polymorph from each reactive trajectory. This deep learning-assisted comprehensive analysis offers an alternative view of crystal nucleation mechanisms and pathways.
- [2] arXiv:2405.09669 [pdf, other]
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Title: Bounds on Fluctuations of First Passage Times for Counting Observables in Classical and Quantum Markov ProcessesSubjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
We study the statistics of first passage times (FPTs) of trajectory observables in both classical and quantum Markov processes. We consider specifically the FPTs of counting observables, that is, the times to reach a certain threshold of a trajectory quantity which takes values in the positive integers and is non-decreasing in time. For classical continuous-time Markov chains we rigorously prove: (i) a large deviation principle (LDP) for FPTs, whose corollary is a strong law of large numbers; (ii) a concentration inequality for the FPT of the dynamical activity, which provides an upper bound to the probability of its fluctuations to all orders; and (iii) an upper bound to the probability of the tails for the FPT of an arbitrary counting observable. For quantum Markov processes we rigorously prove: (iv) the quantum version of the LDP, and subsequent strong law of large numbers, for the FPTs of generic counts of quantum jumps; (v) a concentration bound for the the FPT of total number of quantum jumps, which provides an upper bound to the probability of its fluctuations to all orders, together with a similar bound for the sub-class of quantum reset processes which requires less strict irreducibility conditions; and (vi) a tail bound for the FPT of arbitrary counts. Our results allow to extend to FPTs the so-called "inverse thermodynamic uncertainty relations" that upper bound the size of fluctuations in time-integrated quantities. We illustrate our results with simple examples.
- [3] arXiv:2405.09728 [pdf, other]
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Title: Hidden zero modes and topology of multiband non-Hermitian systemsSubjects: Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
In a finite non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has lead to misconceptions about the topological protection of edge modes in such systems. Here we show why this breakdown does occur and that it typically results in hidden zero modes, extremely long-lived zero energy excitations, which are only revealed when considering the singular value instead of the eigenvalue spectrum. We point out, furthermore, that in a finite multiband non-Hermitian system with Hamiltonian $H$, one needs to consider also the reflected Hamiltonian $\tilde H$, which is in general distinct from the adjoint $H^\dagger$, to properly relate the number of protected zeroes to the winding number of $H$.
- [4] arXiv:2405.09850 [pdf, other]
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Title: Thermally activated particle motion in biased correlated Gaussian disorder potentialsComments: 9 pages, 6 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn)
Thermally activated particle motion in disorder potentials is controlled by the large-$\Delta V$ tail of the distribution of height $\Delta V$ of the potential barriers created by the disorder. We employ the optimal fluctuation method to evaluate this tail for correlated quenched Gaussian potentials in one dimension in the presence of a small bias of the potential. We focus on the mean escape time (MET) of overdamped particles averaged over the disorder. We show that the bias leads to a strong (exponential) reduction of the MET in the direction along the bias. The reduction depends both on the bias, and on detailed properties of the covariance of the disorder, such as its derivatives and asymptotic behavior at large distances. We verify our theoretical predictions, as well as earlier predictions for zero bias, by performing large-deviation simulations of the potential disorder. The simulations employ correlated random potential sampling based on the circulant embedding method and the Wang-Landau algorithm, which enable us to probe probability densities smaller than $10^{-1200}$.
- [5] arXiv:2405.10095 [pdf, other]
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Title: Nonuniversal critical dynamics on planar random lattices with heterogeneous degree distributionsComments: 7 pages, 7 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech)
The weighted planar stochastic (WPS) lattice introduces a topological disorder that emerges from a multifractal structure. Its dual network has a power-law degree distribution and is embedded in a two-dimensional space, forming a planar network. We modify the original recipe to construct WPS networks with degree distributions interpolating smoothly between the original power-law tail, $P(q)\sim q^{-\alpha}$ with exponent $\alpha\approx 5.6$, and a square lattice. We analyze the role of disorder in the modified WPS model, considering the critical behavior of the contact process. We report a critical scaling depending on the network degree distribution. The scaling exponents differ from the standard mean-field behavior reported for CP on infinite-dimensional (random) graphs with power-law degree distribution. Furthermore, the disorder present in the WPS lattice model is in agreement with the Luck-Harris criterion for the relevance of disorder in critical dynamics. However, despite the same wandering exponent $\omega=1/2$, the disorder effects observed for the WPS lattice are weaker than those found for uncorrelated disorder.
- [6] arXiv:2405.10181 [pdf, other]
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Title: Phase behavior of metastable water from large-scale simulations of a quantitative accurate model: The liquid-liquid critical pointComments: 18 pages, 3 tables, and 12 figures. Submitted to The Journal of Chemical PhysicsSubjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft)
Water's unique anomalies are vital in various applications and biological processes, yet the molecular mechanisms behind these anomalies remain debated, particularly in the metastable liquid phase under supercooling and stretching conditions. Experimental challenges in these conditions have led to simulations suggesting a liquid-liquid phase transition between low-density and high-density water phases, culminating in a liquid-liquid critical point (LLCP). However, these simulations are limited by computational expense, small system sizes, and reliability of water models. Using the FS model, we improve accuracy in predicting water's density and response functions across a broad range of temperatures and pressures. The FS model avoid by design first-order phase transitions towards crystalline phases, allowing thorough exploration of the metastable phase diagram. We employ advanced numerical techniques to bypass dynamical slowing down and perform finite-size scaling on systems significantly larger than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, accurately demonstrating the existence of the LLCP in the 3D Ising universality class at TC = 186 +/- 4 K and PC = 174 +/- 14 MPa, following a liquid-liquid phase separation below 200 MPa. These predictions align with recent experimental data and more sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. Moreover, we observe that the hydrogen bond network exhibits substantial cooperative fluctuations at scales larger than 10 nm, even at temperatures relevant to biopreservation. These findings have significant implications for fields such as nanotechnology and biophysics, offering new insights into water's behavior under varied conditions.
- [7] arXiv:2405.10283 [pdf, other]
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Title: Power-law relaxation of a confined diffusing particle subject to resetting with memoryComments: 19 pages, 3 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech)
We study the relaxation of a Brownian particle with long range memory under confinement in one dimension. The particle diffuses in an arbitrary confining potential and resets at random times to previously visited positions, chosen with a probability proportional to the local time spend there by the particle since the initial time. This model mimics an animal which moves erratically in its home range and returns preferentially to familiar places from time to time. The steady state density of the position is given by the equilibrium Boltzmann-Gibbs distribution, as in standard diffusion, while the transient part of the density can be obtained through a mapping of the Fokker-Planck equation of the process to a Schr\"odinger eigenvalue problem. Due to memory, the approach at large time toward the steady state is critically self-organised, in the sense that it always follows a sluggish power-law form, in contrast to the exponential decay that characterises Markov processes. The exponent of this power-law depends in a simple way on the resetting rate and on the relaxation rate of the Brownian particle in the absence of resetting. We apply these findings to several exactly solvable examples, such as the harmonic, V-shaped and box potentials.
Cross-lists for Fri, 17 May 24
- [8] arXiv:2405.08374 (cross-list from math-ph) [pdf, ps, other]
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Title: On Long Range Ising Models with Random Boundary ConditionsComments: 53 pagesSubjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR)
We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power $2-\alpha$ (for $0 \leq \alpha < 1$), and prepared with randomly chosen boundary conditions. We show that at low temperatures in the thermodynamic limit the finite-volume Gibbs measures do not converge, but have a distributional limit, the so-called metastate. We find that there is a distinction between the values of $\alpha$ less than or larger than $\frac{1}{2}$. For moderate, or intermediate, decay $\alpha < \frac{1}{2}$, the metastate is very dispersed and supported on the set of all Gibbs measures, both extremal and non-extremal, whereas for slow decays $\alpha > \frac{1}{2}$ the metastate is still dispersed, but has its support just on the set of the two extremal Gibbs measures, the plus measure and the minus measure.
The former, moderate decays case, appears to be new and is due to the occurrence of almost sure boundedness of the random variable which is the sum of all interaction (free) energies between random and ordered half-lines, when the decay is fast enough, but still slow enough to get a phase transition ($\alpha>0$); while the latter, slow decays case, is more reminiscent of and similar to the behaviour of higher-dimensional nearest-neighbour Ising models with diverging boundary (free) energies.
We leave the threshold case $\alpha=\frac{1}{2}$ for further studies. - [9] arXiv:2405.08467 (cross-list from quant-ph) [pdf, other]
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Title: Equilibrium Propagation: the Quantum and the Thermal CasesSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI)
Equilibrium propagation is a recently introduced method to use and train artificial neural networks in which the network is at the minimum (more generally extremum) of an energy functional. Equilibrium propagation has shown good performance on a number of benchmark tasks. Here we extend equilibrium propagation in two directions. First we show that there is a natural quantum generalization of equilibrium propagation in which a quantum neural network is taken to be in the ground state (more generally any eigenstate) of the network Hamiltonian, with a similar training mechanism that exploits the fact that the mean energy is extremal on eigenstates. Second we extend the analysis of equilibrium propagation at finite temperature, showing that thermal fluctuations allow one to naturally train the network without having to clamp the output layer during training. We also study the low temperature limit of equilibrium propagation.
- [10] arXiv:2405.09613 (cross-list from quant-ph) [pdf, other]
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Title: Computable entanglement costComments: 7+24 pages, no figuresSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
Quantum information theory is plagued by the problem of regularisations, which require the evaluation of formidable asymptotic quantities. This makes it computationally intractable to gain a precise quantitative understanding of the ultimate efficiency of key operational tasks such as entanglement manipulation. Here we consider the problem of computing the asymptotic entanglement cost of preparing noisy quantum states under quantum operations with positive partial transpose (PPT). A previously claimed solution to this problem is shown to be incorrect. We construct instead an alternative solution in the form of two hierarchies of semi-definite programs that converge to the true asymptotic value of the entanglement cost from above and from below. Our main result establishes that this convergence happens exponentially fast, thus yielding an efficient algorithm that approximates the cost up to an additive error $\varepsilon$ in time $\mathrm{poly}\big(D,\,\log(1/\varepsilon)\big)$, where $D$ is the underlying Hilbert space dimension. To our knowledge, this is the first time that an asymptotic entanglement measure is shown to be efficiently computable despite no closed-form formula being available.
- [11] arXiv:2405.09614 (cross-list from hep-th) [pdf, other]
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Title: Positivity bounds on electromagnetic properties of mediaComments: 27 pages + appendices, 7 figuresSubjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium -- the macroscopic Maxwell equations -- can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities $\varepsilon(\omega,|\boldsymbol{k}|)$ and $\mu(\omega,|\boldsymbol{k}|)$. Microcausality implies analyticity of the retarded Green's functions when the imaginary part of the $4$-vector $(\omega,\boldsymbol{k})$ lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, $\varepsilon(0,0)$ and $\mu(0,0)$. In particular the quantities $\varepsilon(0,0)-1$ and $\varepsilon(0,0) - 1/\mu(0,0)$ are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior.
- [12] arXiv:2405.09628 (cross-list from quant-ph) [pdf, other]
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Title: Quantum Dynamics in Krylov Space: Methods and ApplicationsAuthors: Pratik Nandy, Apollonas S. Matsoukas-Roubeas, Pablo Martínez-Azcona, Anatoly Dymarsky, Adolfo del CampoComments: 64 pages, 27 figures. arXiv admin note: text overlap with arXiv:1802.02633 by other authorsSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD)
The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide a compact and computationally efficient description of quantum evolution, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems.
- [13] arXiv:2405.09745 (cross-list from hep-th) [pdf, other]
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Title: Pseudoentropy sum rule by analytical continuation of the superposition parameterComments: 33 pagesSubjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of a superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo R\'enyi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.
- [14] arXiv:2405.10062 (cross-list from cond-mat.dis-nn) [pdf, other]
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Title: Phenomenology of many-body localization in bond-disordered spin chainsComments: comments most welcome!!!Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
Many-body localization (MBL) hinders the thermalization of quantum many-body systems in the presence of strong disorder. In this work, we study the MBL regime in bond-disordered spin-1/2 XXZ spin chain, finding the multimodal distribution of entanglement entropy in eigenstates, sub-Poissonian level statistics, and revealing a relation between operators and initial states required for examining the breakdown of thermalization in the time evolution of the system. We employ a real space renormalization group scheme to identify these phenomenological features of the MBL regime that extend beyond the standard picture of local integrals of motion relevant for systems with disorder coupled to on-site operators. Our results pave the way for experimental probing of MBL in bond-disordered spin chains.
Replacements for Fri, 17 May 24
- [15] arXiv:2302.08459 (replaced) [pdf, other]
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Title: Overlap renormalization group transformations for disordered systemsAuthors: Dimitrios BachtisSubjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Computational Physics (physics.comp-ph)
- [16] arXiv:2310.06698 (replaced) [pdf, other]
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Title: Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum AnnealerComments: 12 + 6 pages, 7 + 8 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
- [17] arXiv:2311.06478 (replaced) [pdf, other]
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Title: Reduced Dimensional Monte Carlo Method: Preliminary IntegrationsJournal-ref: Phys. Rev. E 109, 045308 (2024)Subjects: Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
- [18] arXiv:2402.06343 (replaced) [pdf, ps, other]
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Title: Blackbody heat capacity at constant pressureAuthors: E. S. Moreira JrComments: 8 pages, no figures. Version accepted for publication in JSTATSubjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
- [19] arXiv:2204.00921 (replaced) [pdf, other]
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Title: Effects of self-avoidance on the packing of stiff rods on ellipsoidsSubjects: Soft Condensed Matter (cond-mat.soft); Materials Science (cond-mat.mtrl-sci); Statistical Mechanics (cond-mat.stat-mech); Adaptation and Self-Organizing Systems (nlin.AO)
- [20] arXiv:2310.16709 (replaced) [pdf, other]
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Title: Sampling reduced density matrix to extract fine levels of entanglement spectrumSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
- [21] arXiv:2311.18005 (replaced) [pdf, ps, other]
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Title: Exact fixed-point tensor network construction for rational conformal field theoryComments: 12 pages, 13 figures, 4 tables; typos corrected, references added, more data included in AppendixSubjects: Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)
- [22] arXiv:2403.07565 (replaced) [pdf, other]
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Title: Logarithmic critical slowing down in complex systems: from statics to dynamicsComments: 22 pages, 2 figuresSubjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci); Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech)
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