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arXiv2017

Rattler-induced aging dynamics in jammed granular systems

Granular materials jam when developing a network of contact forces able to resist the applied stresses. Through numerical simulations of the dynamics of the jamming process, we show that the jamming transition does not occur when the kinetic energy vanishes. Rather, as the system jams, the kinetic energy becomes dominated by rattlers particles, that scatter withing their cages. The relaxation of the kinetic energy in the jammed configuration exhibits a double power-law decay, which we interpret in terms of the interplay between backbone and rattlers particles.

cond-mat.stat-mech↗

arXiv2017

Bubble nucleation in disordered Landau-Ginzburg model

In this paper we investigate bubble nucleation in a disordered Landau-Ginzburg model. First we adopt the standard procedure to average over the disordered free energy. This quantity is represented as a series of the replica partition functions of the system. Using the saddle-point equations in each replica partition function, we discuss the presence of a spontaneous symmetry breaking mechanism. The leading term of the series is given by a large-N Euclidean replica field theory. Next, we consider finite temperature effects. Below some critical temperature, there are N real instantons-like solutions in the model. The transition from the false to the true vacuum for each replica field is given by the nucleation of a bubble of the true vacuum. In order to describe these irreversible processes of multiple nucleation, going beyond the diluted instanton approximation, an effective model is constructed, with one single mode of a bosonic field interacting with a reservoir of N identical two-level systems.

cond-mat.stat-mech↗

arXiv2018

Role of thermal expansion heterogeneity in the cryogenic rejuvenation of metallic glasses

Cryogenic rejuvenation in metallic glasses reported in Ketov et al 's experiment (Nature(2015)524,200) has attracted much attention, both in experiments and numerical studies. The atomic mechanism of rejuvenation has been conjectured to be related to the heterogeneity of the glassy state, but the quantitative evidence is still elusive. Here we use molecular dynamics simulations of a model metallic glass to investigate the heterogeneity in the local thermal expansion. We then combine the resulting spatial distribution of thermal expansion with a continuum mechanics calculation to infer the internal stresses caused by a thermal cycle. Comparing the internal stress with the local yield stress, we prove that the heterogeneity in thermomechanical response has the potential to trigger local shear transformations, and therefore to induce rejuvenation during a cryogenic thermal cycling.

cond-mat.dis-nn↗

arXiv2018

Driven nonlinear nanomechanical resonators as digital signal detectors

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities.

cond-mat.mes-hall↗

arXiv2018

On Global-in-time Chaotic Weak Solutions of the Liouville Equation for Hard Spheres

We outline a new method of construction of global-in-time weak solutions of the Liouville equation - and also of the associated BBGKY hierarchy - corresponding to the hard sphere singular Hamiltonian. Our method makes use only of geometric reflection arguments on phase space. As a consequence of our method, in the case of $N=2$ hard spheres, we show for any chaotic initial data, the unique global-in-time weak solution $F$ of the Liouville equation is realised as $F=\mathsf{R}(f\otimes f)$ in the sense of tempered distributions on $T\mathbb{R}^{6}\times (-\infty, \infty)$, where $\mathsf{R}$ is a 'reflection-type' operator on Schwartz space, and $f$ is a global-in-time classical solution of the 1-particle free transport Liouville equation on $T\mathbb{R}^{3}$.

math.AP↗

arXiv2018

Application of the fluctuation theorem to motor proteins: from F1-ATPase to axonal cargo transport by kinesin and dynein

The fluctuation theorem is a representative theorem in non-equilibrium statistical physics actively studied in the 1990's. Relating to entropy production in non-equilibrium states, the theorem has been used to estimate the driving power of motor proteins from fluctuation in their motion. In this review, usage of the fluctuation theorem in experiments on motor proteins is illustrated for biologists, especially those who study mechanobiology, in which force measurement is a central issue. We first introduce the application of the fluctuation theorem in measuring the rotary torque of the rotary motor protein F1-ATPase. Next, as an extension of this application, a recent trial estimating the force generated during cargo transport in vivo by the microtubule motors kinesin and dynein is introduced. Elucidation of the physical mechanism of such transport is important, especially for neurons, in which deficits in cargo transport are deeply related to neuronal diseases. Finally, perspectives on the fluctuation theorem as a new technique in the field of neuroscience are discussed.

physics.bio-ph↗

arXiv2018

Stationarity and energy transfer in out-of-equilibrium systems

We define a characteristic energy density based on the measurement of the two first moments of the extrinsic injected power smoothed over time. Using the stationarity, we show that this definition characterizes an energy per degrees freedom of the intrinsic dissipation. Our framework can be applied to systems in contact with thermostats put out of equilibrium by an external driving but it holds also for intrinsically dissipative macroscopic systems that go at rest when the forcing is stopped. Moreover, we are not concerned about the fluctuations around zero of the smoothed injected power that can be extremely rare and difficult to catch experimentally. Then we show that the characteristic energy density we defined, reduces to the kinetic energy of a Brownian-like particle described by a set of Langevin equations with a viscous damping term. The particle can be either in contact with a thermostat or intrinsically dissipative and driven by a random force. In the first case, we recover the result obtained in the framework of the fluctuation relation but extended to a correlated thermal noise. Our characteristic energy density is measured in an experimental system of nonlinear waves generated by a large shaker in a thin elastic plate. A smaller shaker attached to the moving plate is used as a probe to measure the energy exchanged with the plate excited by the large shaker. For both, the proportionality of our characteristic energy density with the kinetic energy is demonstrated. It is a consequence of the viscous damping driving the dissipation in this system. Another system with nonlinear frictional dissipation is investigated numerically model. In this case, our definition of energy density deduced from fluctuations of injected power still characterizes the dissipation but is no more proportional to the kinetic energy because the dissipative process is not a viscous damping.

cond-mat.stat-mech↗

arXiv2021

Stochastic dynamics without detailed balance condition connecting simple gradient method and Hamiltonian Monte Carlo

Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the acceleration of convergence to the target distribution. Hamiltonian Monte Carlo (HMC) is such a variant of MCMC. In the recent development of MCMC, another approach based on the violation of the detailed balance condition has attracted much attention. Historically, these two approaches have been proposed independently, and their relationship has not been clearly understood. In this paper, the two approaches are seamlessly understood in the framework of generalized Monte Carlo method that violates the detailed balance condition. Furthermore we propose an efficient Monte Carlo method based on our framework.

cond-mat.stat-mech↗

arXiv2022

Tensor-Network Approach to Work Statistics for 1D Quantum Lattice Systems

We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block Decimation (TEBD) and Minimally Entangled Typical Thermal States (METTS). The former is an efficient algorithm used to simulate the dynamics of 1D quantum lattice systems, while the latter a finite-temperature algorithm for generating a set of typical states representing the Gibbs canonical ensemble. As an illustrative example, we apply this approach to the Ising chain in mixed transverse and longitudinal fields. Under an arbitrary protocol, the moment generating function of the work can be obtained, from which the work moments are numerically calculated and the quantum Jarzynski equality can be tested. Moreover, the numerical approach is also adapted to test the universal quantum work relation involving a functional of an arbitrary observable.

cond-mat.stat-mech↗

arXiv2024

Collective quantum phases in frustrated arrays of Josephson junctions

We study collective quantum phases and quantum phase transitions occurring in frustrated sawtooth arrays of small quantum Josephson junctions. Frustration is introduced through the periodic arrangement of $0$- and $π$- Josephson junctions with the Josephson coupling energies $αE_\mathrm{J}$ of different signs, $-1\leq α\leq 1$. The complexity of the potential landscape of the system is controlled by the frustration parameter $f=(1-α)/2$. The potential energy has a single global minimum in the non-frustrated regime ($f f_\mathrm{cr}=0.75$). We address the coherent quantum regime and identify several collective quantum phases: disordered (insulating) and ordered (superconducting) phases in the non-frustrated regime, as well as highly entangled patterns of vortices and anti-vortices in the frustrated regime. These collective quantum phases are controlled by several physical parameters: the frustration $f$, the Josephson coupling, and the charging energies of junctions and islands. We map the control parameter phase diagram by characterizing the quantum dynamics of frustrated Josephson junction arrays by spatially and temporally resolved quantum-mechanical correlation function of the local magnetization.

cond-mat.str-el↗

arXiv2025

Self-sustained frictional cooling in active matter

Cooling processes in nature are typically generated by external contact with a cold reservoir or bath. According to the laws of thermodynamics, the final temperature of a system is determined by the temperature of the environment. Here, we report a spontaneous internal cooling phenomenon for active particles, occurring without external contact. This effect, termed ``self-sustained frictional cooling'', arises from the interplay between activity and dry (Coulomb) friction, and in addition is self-sustained from particles densely caged by their neighbors. If an active particle moves in its cage, dry friction will stop any further motion after a collision with a neighbor particle thus cooling the particle down to an extremely low temperature. We demonstrate and verify this self-sustained cooling through experiments and simulations on active granular robots and identify dense frictional arrested clusters coexisting with hot, dilute regions. Our findings offer potential applications in two-dimensional swarm robotics, where activity and dry friction can serve as externally tunable mechanisms to regulate the swarm's dynamical and structural properties.

cond-mat.soft↗

arXiv2026

Deterministic construction of typical networks in network models

In network science, one often wants to say that a given real-world network appears to come from a particular network model. In statistical physics, the corresponding problem is about how typical a given state, representing real-world data, is in a particular statistical ensemble. One way to address this problem is to measure the distance between the data and the most typical state in the ensemble. Here, we identify the conditions that allow us to define this most typical state. These conditions hold in a wide class of grand canonical ensembles and their random mixtures. Our main contribution is a deterministic construction of a state that converges to this most typical state in the thermodynamic limit. This construction involves rounds of derandomization procedures, some of which deal with derandomizing point processes, an uncharted territory. We illustrate the construction on one particular network model, deterministic hyperbolic graphs, and its application to real-world networks, many of which we find are close to the most typical network in the model. While our main focus is on network models, our results are very general and apply to any grand canonical ensembles and their random mixtures satisfying certain niceness requirements.

physics.soc-ph↗

arXiv2026

Density of states of quantum systems from free probability theory: a brief overview

We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random matrix Hamiltonian, which can be written as a sum of two non-commutating operators, one can obtain an expression for the density of states of the Hamiltonian from the known density of states of the two component operators by assuming that these operators are mutually free and by using the free additive convolution. In many examples of interacting quantum systems and random matrix models, this procedure is known to provide a reasonably accurate approximation to the exact numerical density of states. We review some of the examples that are known in the literature where this procedure works very well, and also discuss some of the limitations of this method in situations where the free probability approximation fails to provide a sufficiently accurate description of the exact density of states. Subsequently, we describe a perturbation scheme that can be developed from the subordination formulas for the Cauchy transform of the density of states and use it to obtain approximate analytical expressions for the density of states in various models, such as the Rosenzweig-Porter random matrix ensemble and the Anderson model with on-site disorder.

quant-ph↗

arXiv2013

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. Based on the emergent symmetry Z_2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. We perform an extensive Density Matrix Renormalization Group analysis of the behaviour at criticality and evaluate the critical exponents and the central charge with high precision. We thus provide strong numerical evidence confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

cond-mat.stat-mech↗

arXiv2011

On Evolution Equations for Marginal Correlation Operators

This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann hierarchy for correlation operators that give an alternative approach to the description of states in comparison with the density operators. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed.

math-ph↗

arXiv2013

The stability of a graph partition: A dynamics-based framework for community detection

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs, which can provide insight into the structure and function of the overall system. Sparked by seminal work by Newman and Girvan, an interesting line of research has been devoted to investigating modular community structure in networks, revitalising the classic problem of graph partitioning. However, modular or community structure in networks has notoriously evaded rigorous definition. The most accepted notion of community is perhaps that of a group of elements which exhibit a stronger level of interaction within themselves than with the elements outside the community. This concept has resulted in a plethora of computational methods and heuristics for community detection. Nevertheless a firm theoretical understanding of most of these methods, in terms of how they operate and what they are supposed to detect, is still lacking to date. Here, we will develop a dynamical perspective towards community detection enabling us to define a measure named the stability of a graph partition. It will be shown that a number of previously ad-hoc defined heuristics for community detection can be seen as particular cases of our method providing us with a dynamic reinterpretation of those measures. Our dynamics-based approach thus serves as a unifying framework to gain a deeper understanding of different aspects and problems associated with community detection and allows us to propose new dynamically-inspired criteria for community structure.

physics.soc-ph↗

arXiv2012

Open Quantum Systems. An Introduction

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.

quant-ph↗

arXiv2013

A linear nonequilibrium thermodynamics approach to optimization of thermoelectric devices

Improvement of thermoelectric systems in terms of performance and range of applications relies on progress in materials science and optimization of device operation. In this chapter, we focuse on optimization by taking into account the interaction of the system with its environment. For this purpose, we consider the illustrative case of a thermoelectric generator coupled to two temperature baths via heat exchangers characterized by a thermal resistance, and we analyze its working conditions. Our main message is that both electrical and thermal impedance matching conditions must be met for optimal device performance. Our analysis is fundamentally based on linear nonequilibrium thermodynamics using the force-flux formalism. An outlook on mesoscopic systems is also given.

physics.class-ph↗