# Statistical Mechanics

## New submissions

[ total of 23 entries: 1-23 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Wed, 30 Nov 22

[1]
Title: Single active particle in a harmonic potential: non-existence of the Jarzynski relation
Authors: Grzegorz Szamel
Subjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft)

The interest in active matter stimulates the need to generalize thermodynamic description and relations to active matter systems, which are intrinsically out of equilibrium. One important example is the Jarzynski relation, which links the exponential average of work done in an arbitrary process connecting two equilibrium states with the difference of the free energies of these states. Using a simple model system, a single thermal active Ornstein-Uhlenbeck particle in a harmonic potential, we show that if the standard stochastic thermodynamics definition of work is used, the Jarzynski relation is not generally valid for processes between stationary states of active matter systems.

[2]
Title: Yukawa Friedel-Tail pair potentials for warm dense matter applications
Subjects: Statistical Mechanics (cond-mat.stat-mech); Plasma Physics (physics.plasm-ph)

Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard $N$-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the non-parametric force-matched potentials from $N$-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multi-species warm dense matter.

[3]
Title: Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation
Subjects: Statistical Mechanics (cond-mat.stat-mech); Soft Condensed Matter (cond-mat.soft); Biological Physics (physics.bio-ph)

Abstract Entropy production plays an important role in the regulation and stability of active matter systems, and its rate quantifies the nonequilibrium nature of these systems. However, entropy production is hard to be experimentally estimated even in some simple active systems like molecular motors or bacteria, which may be modeled by the run-and-tumble particle (RTP), a representative model in the study of active matters. Here we resolve this problem for an asymmetric RTP in one-dimension, firstly constructing a finite time thermodynamic uncertainty relation (TUR) for a RTP, which works well in the short observation time regime for entropy production estimation. Nevertheless, when the activity dominates,i.e., the RTP is far from equilibrium, the lower bound for entropy production from TUR turns to be trivial. We address this issue by introducing a recently proposed high-order thermodynamic uncertainty relation (HTUR), in which the cumulant generating function of current serve as a key ingredient. To exploit the HTUR, we adopt a novel method to analytically obtain the cumulant generating function of the current we study, with no need to explicitly know the time-dependent probability distribution. The HTUR is demonstrated to be able to estimate the steady state energy dissipation rate accurately because the cumulant generating function covers higher-order statistics of the current, including rare and large fluctuations besides its variance. Compared to the conventional TUR, the HTUR could give significantly improved estimation of energy dissipation, which can work well even in the far-from equilibrium regime. We also provide a strategy based on the improved bound to estimate the entropy production from moderate amount of trajectory data for experimental feasibility.

[4]
Title: The cubic fixed point in three dimensions: Monte Carlo simulations of the $φ^4$ model on the lattice
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th)

We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $\phi^4$ model on the simple cubic lattice. We generalize the idea of improved models to a two-parameter family of models. The two-parameter space is scanned for the point, where the amplitudes of the two leading corrections to scaling vanish. To this end, a dimensionless quantity is introduced that monitors the breaking of the $O(N)$-invariance. For $N=4$, we determine the correction exponents $\omega_1=0.763(24)$ and $\omega_2=0.082(5)$. In the case of $N=3$, we obtain $Y_4=0.0142(6)$ for the RG-exponent of the cubic perturbation at the $O(3)$-invariant fixed point, while the correction exponent $\omega_2=0.0133(8)$ at the cubic fixed point. Simulations close to the improved point result in the estimates $\nu=0.7202(7)$ and $\eta=0.0371(2)$ of the critical exponents of the cubic fixed point for $N=4$. For $N=3$, at the cubic fixed point, the $O(3)$-symmetry is only mildly broken and the critical exponents differ only by little from those of the $O(3)$-invariant fixed point. We find $-0.00001 \lessapprox \eta_{cubic}- \eta_{O(3)} \lessapprox 0.00007$ and $\nu_{cubic}-\nu_{O(3)} =-0.00061(10)$.

[5]
Title: Effects of mortality on stochastic search processes with resetting
Subjects: Statistical Mechanics (cond-mat.stat-mech)

We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $\mu$, diffusing in one dimension. The particle starts its motion from $x>0$ and it is subject to stochastic resetting with constant rate $r$. We first show that the probability of reaching the target is closely related to the mean first-passage time of the corresponding problem in absence of mortality. We then consider the mean and the variance of the first-passage time conditioned on the event that the particle reaches the target before dying. When the average lifetime $\tau_\mu=1/\mu$ satisfies $\tau_\mu>\alpha\tau_D$, where $\tau_D=x^2/(4D)$ is the diffusive time scale and $\alpha\approx1.575$ is a constant, there is a resetting rate $r_\mu^*$ that maximizes the probability, and there may also be a different rate $r_m$ that minimizes the average time of a successful search; on the other hand, for average lifetimes $\tau_\mu<\beta\tau_D$, with $\beta\approx0.2884$, resetting progressively eliminates slower search processes, resulting in decreasing mean first-passage times but also decreasing the probability of success. Intermediate regimes are also considered.

[6]
Title: Self-avoiding walks and polygons confined to a square
Authors: S G Whittington
Subjects: Statistical Mechanics (cond-mat.stat-mech)

We prove two rigorous results about the asymptotic behaviour of the numbers of polygons and self-avoiding walks confined to a square on the square lattice. Specifically we prove that the dominant asymptotic behaviour of polygons confined to an LxL square is identical to that of self-avoiding walks that cross an LxL square from one corner vertex to the opposite corner vertex. We also prove a result about the subdominant asymptotic behaviour of self-avoiding walks crossing a square and extend this result to self-avoiding walks crossing a hypercube in the d-dimensional hypercubic lattice.

[7]
Title: Optimal power extraction from active particles with hidden states
Comments: 6 pages (main) + 9 pages (SM), 4 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech)

We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that the instantaneous velocity, but not the fluctuating self-propulsion velocity, is accessible to direct observation. Our Bayesian approach draws on the Onsager-Machlup path integral formalism and is exemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeck dynamics in one dimension. Such optimal protocols extract positive work even in models characterised by time-symmetric positional trajectories and thus vanishing informational entropy production rates. We argue that the theoretical bounds derived in this work are those against which the performance of realistic active matter engines should be compared.

### Cross-lists for Wed, 30 Nov 22

[8]  arXiv:2211.15690 (cross-list from cond-mat.str-el) [pdf, other]
Title: Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose couplings decay with a power-law exponent $\alpha$, there has been no systematic study for a free-fermion symmetry class. We introduce a technique for solving gapped, translationally invariant models in the 1D BDI and AIII symmetry classes with $\alpha>1$, linking together the quantized winding invariant, bulk topological string-order parameters and a complete solution of the edge modes. The physics of these chains is elucidated by studying a complex function determined by the couplings of the Hamiltonian: in contrast to the short-range case where edge modes are associated to roots of this function, we find that they are now associated to singularities. A remarkable consequence is that the finite-size splitting of the edge modes depends on the topological winding number, which can be used as a probe of the latter. We furthermore generalise these results by (i) identifying a family of BDI chains with $\alpha<1$ where our results still hold, and (ii) showing that gapless symmetry-protected topological chains can have topological invariants and edge modes when $\alpha -1$ exceeds the dynamical critical exponent.

[9]  arXiv:2211.15872 (cross-list from quant-ph) [pdf, other]
Title: Scrambling and quantum chaos indicators from long-time properties of operator distributions
Comments: Main text: 14 pages, 7 figures. Appendices: 3 pages, 3 figures
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases, and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

[10]  arXiv:2211.16240 (cross-list from math-ph) [pdf, other]
Title: Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions
Comments: 42 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2011.05148
Journal-ref: J.Phys.A: Math.Theor. 55 (2022) 225002 (37 pp) Journal of Physics A: Mathematical and Theoretical, Volume 55, Number 22 (2022) 225002
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Combinatorics (math.CO)

Relations between the mean values of distributions of flipped spins on periodic Heisenberg XX chain and some aspects of enumerative combinatorics are discussed. The Bethe vectors, which are the state-vectors of the model, are considered both as on- and off-shell. It is this approach that makes it possible to represent and to study the correlation functions in the form of non-intersecting nests of lattice walks and related plane partitions. We distinguish between two types of walkers, namely lock step models and random turns. Of particular interest is the connection of random turns walks and a circulant matrix. The determinantal representation for the norm-trace generating function of plane partitions with fixed height of diagonal parts is obtained as the expectation of the generating exponential over off-shell N-particle Bethe states. The asymptotics of the dynamical mean value of the generating exponential is calculated in the double scaling limit provided that the evolution parameter is large. It is shown that the amplitudes of the leading asymptotics depend on the number of diagonally constrained plane partitions.

[11]  arXiv:2211.16288 (cross-list from cond-mat.soft) [pdf, other]
Title: Shear jamming and fragility in fractal suspensions under confinement
Comments: S.I. included, In press Soft Matter (2022)
Subjects: Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech); Fluid Dynamics (physics.flu-dyn)

Under applied stress, the viscosity of many dense particulate suspensions increases drastically, a response known as discontinuous shear-thickening (DST). In some cases, the applied stress can even transform the suspension into a solid-like shear jammed state. Although shear jamming (SJ) has been probed for dense suspensions with particles having well-defined shapes, such a phenomenon for fractal objects has not been explored. Here, using rheology and in situ optical imaging, we study the flow behaviour of ultra-dilute fractal suspensions of multi-walled carbon nanotubes (MWCNT) under confinement. We show a direct transition from flowing to SJ state without a precursory DST in fractal suspensions at an onset volume fraction, $\phi \sim$ 0.5\%, significantly lower than that of conventional dense suspensions ($\phi \sim$ 55\%). The ultra-low concentration enables us to demonstrate the fragility and associated contact dynamics of the SJ state, which remain experimentally unexplored in suspensions. Furthermore, using a generalized Wyart-Cates model, we propose a generic phase diagram for fractal suspensions that captures the possibility of SJ without prior DST over a wide range of shear stress and volume fractions.

[12]  arXiv:2211.16503 (cross-list from hep-th) [pdf, other]
Title: Coupled minimal models revisited
Comments: 4+2 pages, 2 figures, 1 table
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech)

We study coupled unitary Virasoro minimal models in the large rank ($m \rightarrow \infty$) limit. In large $m$ perturbation theory, we find two non-trivial IR fixed points which exhibit irrational coefficients in several anomalous dimensions and the central charge. For $N>4$ copies, we show that the IR theory breaks all possible currents that would otherwise enhance the Virasoro algebra, up to spin 10. This provides strong evidence that the IR fixed points are examples of compact, unitary, irrational CFTs with the minimal amount of chiral symmetry. We also analyze anomalous dimension matrices for a family of degenerate operators with increasing spin. These display further evidence of irrationality and begin to reveal the form of the leading quantum Regge trajectory.

### Replacements for Wed, 30 Nov 22

[13]  arXiv:2011.09771 (replaced) [pdf, ps, other]
Title: A shortcut way to the Fokker-Planck equation for the non-Markovian dynamics
Subjects: Statistical Mechanics (cond-mat.stat-mech)
[14]  arXiv:2205.03065 (replaced) [pdf, other]
Title: Finite-time bounds on the probabilistic violation of the second law of thermodynamics
Comments: 12 pages, 3 figures, comments welcome. v2 fixed typos and added some more remarks in discussion. Submission to SciPost
Subjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[15]  arXiv:2206.14167 (replaced) [pdf, other]
Title: Ballistic macroscopic fluctuation theory
Comments: v1: 47 pages, 5 figures. v2: 48 pages, 5 figures; generalized proof of the GCFT and the conclusion slightly expanded. v3: 80 pages, 5 figures; single column ver
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[16]  arXiv:2207.01134 (replaced) [pdf, other]
Title: Exact expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble
Comments: 7 pages, 6 figures. This is the version that was accepted for publication in Physical Review E Letters
Journal-ref: Phys. Rev. E 106, L042103 (2022)
Subjects: Statistical Mechanics (cond-mat.stat-mech)
[17]  arXiv:2207.07672 (replaced) [pdf, other]
Title: Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion
Comments: 7 pages, 1 figure. v2: significant improvements to the text, numerous clarifications made. Approach and results unchanged. Version accepted for publications in EPL
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph)
[18]  arXiv:2201.02029 (replaced) [pdf, other]
Title: Optimal Control in Disordered Quantum Systems
Comments: 10 pages, 7 figures, 1 table. Close to published version
Journal-ref: Phys. Rev. Research 4, 043138 (2022)
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[19]  arXiv:2208.05503 (replaced) [pdf, other]
Title: Probing quantum scars and weak ergodicity-breaking through quantum complexity
Comments: v3: typos fixed, published version in Phys. Rev. B
Journal-ref: Phys. Rev. B 106, 205150 (2022)
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
[20]  arXiv:2209.09919 (replaced) [pdf, other]
Title: Bootstrapping the Kronig-Penney Model
Comments: 21 pages, 5 figures, typos corrected, version to appear in Physical Review D
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th)
[21]  arXiv:2211.04055 (replaced) [pdf, other]
Title: Transparent electrodes based on mixtures of nanowires and nanorings: A mean-field approach along with computer simulation
Comments: 9 pages, 9 figures, 3 tables, 42 references, supplement
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[22]  arXiv:2211.06156 (replaced) [pdf, other]
Title: Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular lattice
Comments: 11 pages, 5 figures - Accepted for publication in Phys. Rev. B
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech)
[23]  arXiv:2211.08330 (replaced) [pdf, other]
Title: On Landauer--Büttiker formalism from a quantum quench
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
[ total of 23 entries: 1-23 ]
[ showing up to 2000 entries per page: fewer | more ]

Disable MathJax (What is MathJax?)

Links to: arXiv, form interface, find, cond-mat, recent, 2211, contact, help  (Access key information)