Statistical Mechanics
New submissions
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New submissions for Wed, 30 Nov 22
 [1] arXiv:2211.15714 [pdf, ps, other]

Title: Single active particle in a harmonic potential: nonexistence of the Jarzynski relationAuthors: Grzegorz SzamelComments: 8 pagesSubjects: Statistical Mechanics (condmat.statmech); Soft Condensed Matter (condmat.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 OrnsteinUhlenbeck 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] arXiv:2211.15883 [pdf, other]

Title: Yukawa FriedelTail pair potentials for warm dense matter applicationsComments: 13 figuresSubjects: Statistical Mechanics (condmat.statmech); Plasma Physics (physics.plasmph)
Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many highenergydensity 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 neutralpseudoatom (NPA) approach, a form of singleion density functional theory (DFT), where manyion effects are included via ionion correlation functionals. Standard $N$ion DFTMD 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 nonparametric forcematched potentials from $N$ion DFTMD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or forcematched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for largescale simulations of multispecies warm dense matter.
 [3] arXiv:2211.15973 [pdf, other]

Title: Improving estimation of entropy production rate for runandtumble particle systems by highorder thermodynamic uncertainty relationSubjects: Statistical Mechanics (condmat.statmech); Soft Condensed Matter (condmat.soft); Biological Physics (physics.bioph)
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 runandtumble particle (RTP), a representative model in the study of active matters. Here we resolve this problem for an asymmetric RTP in onedimension, 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 highorder 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 timedependent probability distribution. The HTUR is demonstrated to be able to estimate the steady state energy dissipation rate accurately because the cumulant generating function covers higherorder 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 farfrom 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] arXiv:2211.16170 [pdf, ps, other]

Title: The cubic fixed point in three dimensions: Monte Carlo simulations of the $φ^4$ model on the latticeAuthors: Martin HasenbuschComments: 57 pages, 11 figuresSubjects: Statistical Mechanics (condmat.statmech); High Energy Physics  Lattice (heplat); High Energy Physics  Theory (hepth)
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 twoparameter family of models. The twoparameter 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 RGexponent 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] arXiv:2211.16173 [pdf, ps, other]

Title: Effects of mortality on stochastic search processes with resettingAuthors: Mattia RadiceComments: 13 pages, 4 figuresSubjects: Statistical Mechanics (condmat.statmech)
We study the firstpassage 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 firstpassage time of the corresponding problem in absence of mortality. We then consider the mean and the variance of the firstpassage 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 firstpassage times but also decreasing the probability of success. Intermediate regimes are also considered.
 [6] arXiv:2211.16287 [pdf, ps, other]

Title: Selfavoiding walks and polygons confined to a squareAuthors: S G WhittingtonSubjects: Statistical Mechanics (condmat.statmech)
We prove two rigorous results about the asymptotic behaviour of the numbers of polygons and selfavoiding 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 selfavoiding 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 selfavoiding walks crossing a square and extend this result to selfavoiding walks crossing a hypercube in the ddimensional hypercubic lattice.
 [7] arXiv:2211.16377 [pdf, other]

Title: Optimal power extraction from active particles with hidden statesComments: 6 pages (main) + 9 pages (SM), 4 figuresSubjects: Statistical Mechanics (condmat.statmech)
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 selfpropulsion velocity, is accessible to direct observation. Our Bayesian approach draws on the OnsagerMachlup path integral formalism and is exemplified in the cases of free runandtumble and active OrnsteinUhlenbeck dynamics in one dimension. Such optimal protocols extract positive work even in models characterised by timesymmetric 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.
Crosslists for Wed, 30 Nov 22
 [8] arXiv:2211.15690 (crosslist from condmat.strel) [pdf, other]

Title: Bulkboundary correspondence and singularityfilling in longrange freefermion chainsSubjects: Strongly Correlated Electrons (condmat.strel); Statistical Mechanics (condmat.statmech); Mathematical Physics (mathph); Quantum Physics (quantph)
The bulkboundary correspondence relates topologicallyprotected edge modes to bulk topological invariants, and is wellunderstood for shortrange freefermion chains. Although case studies have considered longrange Hamiltonians whose couplings decay with a powerlaw exponent $\alpha$, there has been no systematic study for a freefermion 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 stringorder 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 shortrange 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 finitesize 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 symmetryprotected topological chains can have topological invariants and edge modes when $\alpha 1$ exceeds the dynamical critical exponent.
 [9] arXiv:2211.15872 (crosslist from quantph) [pdf, other]

Title: Scrambling and quantum chaos indicators from longtime properties of operator distributionsComments: Main text: 14 pages, 7 figures. Appendices: 3 pages, 3 figuresSubjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech)
Scrambling is a key concept in the analysis of nonequilibrium properties of quantum manybody systems. Most studies focus on its characterization via outoftimeordered correlation functions (OTOCs), particularly through the earlytime 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 coarsegrained 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 longtime 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 (crosslist from mathph) [pdf, other]

Title: Spin correlation functions, Ramuslike identities, and enumeration of constrained lattice walks and plane partitionsComments: 42 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2011.05148Journalref: J.Phys.A: Math.Theor. 55 (2022) 225002 (37 pp) Journal of Physics A: Mathematical and Theoretical, Volume 55, Number 22 (2022) 225002Subjects: Mathematical Physics (mathph); Statistical Mechanics (condmat.statmech); High Energy Physics  Theory (hepth); 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 statevectors of the model, are considered both as on and offshell. It is this approach that makes it possible to represent and to study the correlation functions in the form of nonintersecting 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 normtrace generating function of plane partitions with fixed height of diagonal parts is obtained as the expectation of the generating exponential over offshell Nparticle 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 (crosslist from condmat.soft) [pdf, other]

Title: Shear jamming and fragility in fractal suspensions under confinementComments: S.I. included, In press Soft Matter (2022)Subjects: Soft Condensed Matter (condmat.soft); Statistical Mechanics (condmat.statmech); Fluid Dynamics (physics.fludyn)
Under applied stress, the viscosity of many dense particulate suspensions increases drastically, a response known as discontinuous shearthickening (DST). In some cases, the applied stress can even transform the suspension into a solidlike shear jammed state. Although shear jamming (SJ) has been probed for dense suspensions with particles having welldefined 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 ultradilute fractal suspensions of multiwalled 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 ultralow 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 WyartCates 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 (crosslist from hepth) [pdf, other]

Title: Coupled minimal models revisitedComments: 4+2 pages, 2 figures, 1 tableSubjects: High Energy Physics  Theory (hepth); Statistical Mechanics (condmat.statmech)
We study coupled unitary Virasoro minimal models in the large rank ($m \rightarrow \infty$) limit. In large $m$ perturbation theory, we find two nontrivial 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 FokkerPlanck equation for the nonMarkovian dynamicsComments: 33 pagesSubjects: Statistical Mechanics (condmat.statmech)
 [14] arXiv:2205.03065 (replaced) [pdf, other]

Title: Finitetime bounds on the probabilistic violation of the second law of thermodynamicsComments: 12 pages, 3 figures, comments welcome. v2 fixed typos and added some more remarks in discussion. Submission to SciPostSubjects: Statistical Mechanics (condmat.statmech); Quantum Physics (quantph)
 [15] arXiv:2206.14167 (replaced) [pdf, other]

Title: Ballistic macroscopic fluctuation theoryComments: 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 verSubjects: Statistical Mechanics (condmat.statmech); High Energy Physics  Theory (hepth); Mathematical Physics (mathph)
 [16] arXiv:2207.01134 (replaced) [pdf, other]

Title: Exact expressions for the partition function of the onedimensional Ising model in the fixed$M$ ensembleComments: 7 pages, 6 figures. This is the version that was accepted for publication in Physical Review E LettersJournalref: Phys. Rev. E 106, L042103 (2022)Subjects: Statistical Mechanics (condmat.statmech)
 [17] arXiv:2207.07672 (replaced) [pdf, other]

Title: Probabilistic picture for particle number densities in stretched tips of the branching Brownian motionComments: 7 pages, 1 figure. v2: significant improvements to the text, numerous clarifications made. Approach and results unchanged. Version accepted for publications in EPLSubjects: Statistical Mechanics (condmat.statmech); High Energy Physics  Phenomenology (hepph)
 [18] arXiv:2201.02029 (replaced) [pdf, other]

Title: Optimal Control in Disordered Quantum SystemsComments: 10 pages, 7 figures, 1 table. Close to published versionJournalref: Phys. Rev. Research 4, 043138 (2022)Subjects: Quantum Physics (quantph); Disordered Systems and Neural Networks (condmat.disnn); Statistical Mechanics (condmat.statmech)
 [19] arXiv:2208.05503 (replaced) [pdf, other]

Title: Probing quantum scars and weak ergodicitybreaking through quantum complexityComments: v3: typos fixed, published version in Phys. Rev. BJournalref: Phys. Rev. B 106, 205150 (2022)Subjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech); Strongly Correlated Electrons (condmat.strel); High Energy Physics  Theory (hepth)
 [20] arXiv:2209.09919 (replaced) [pdf, other]

Title: Bootstrapping the KronigPenney ModelComments: 21 pages, 5 figures, typos corrected, version to appear in Physical Review DSubjects: Quantum Physics (quantph); Statistical Mechanics (condmat.statmech); Strongly Correlated Electrons (condmat.strel); High Energy Physics  Lattice (heplat); High Energy Physics  Theory (hepth)
 [21] arXiv:2211.04055 (replaced) [pdf, other]

Title: Transparent electrodes based on mixtures of nanowires and nanorings: A meanfield approach along with computer simulationComments: 9 pages, 9 figures, 3 tables, 42 references, supplementSubjects: Disordered Systems and Neural Networks (condmat.disnn); Statistical Mechanics (condmat.statmech)
 [22] arXiv:2211.06156 (replaced) [pdf, other]

Title: Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular latticeComments: 11 pages, 5 figures  Accepted for publication in Phys. Rev. BSubjects: Strongly Correlated Electrons (condmat.strel); Statistical Mechanics (condmat.statmech)
 [23] arXiv:2211.08330 (replaced) [pdf, other]

Title: On LandauerBüttiker formalism from a quantum quenchSubjects: Mesoscale and Nanoscale Physics (condmat.meshall); Statistical Mechanics (condmat.statmech); Mathematical Physics (mathph)
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