Journal of Statistical Physics最新文献

We investigate a multi-walker generalization of the true self-avoiding walk, formulated as a bricklayer model where agents collectively build a growing interface. We investigate the coupled partial differential equations that describe the hydrodynamic limit of this process. Stochastic simulations of N walkers confirm these analytic predictions in the large-N limit, revealing a characteristic parabolic density profile. These results provide a continuum description for the dynamics of non-reversible Monte Carlo algorithms, offering insights into the relaxation mechanisms of collective sampling schemes.

In this article, we initiate the study of operator product expansions (OPEs) for the sine-Gordon model. For simplicity, we focus on the model below the first threshold of collapse ((beta <4pi )) and on the singular terms in OPEs of derivative-type fields (partial varphi ) and (bar{partial }varphi ). We prove that compared to corresponding free field OPEs, the sine-Gordon OPEs develop logarithmic singularities and generate Wick ordered exponentials. Our approach for proving the OPEs relies heavily on Onsager-type inequalities and associated moment bounds for GFF correlation functions involving Wick ordered exponentials of the free field.

We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition requiring that for some iterate each point admits at least one contracting inverse branch. We prove the existence and uniqueness of equilibrium states and the differentiability of statistical quantities (such as the equilibrium states and the free energy function) with respect to the dynamical system.

Recent works proved a hydrodynamic limit for periodically forced atom chains with harmonic interaction and pinning, together with momentum flip [16, 17]. When energy is the only conserved quantity, one would expect similar results in the anharmonic case, as conjectured for the temperature profile and energy flux in [18]. However, outside the harmonic case, explicit computations are generally no longer possible, thus making a rigorous proof of this hydrodynamic limit difficult. Consequently, we numerically investigate the plausibility of this limit for the particular case of a chain with (beta )–FPUT interactions and harmonic pinning. We present our simulation results suggesting that the PDE for the limiting temperature profile and the Green–Kubo type formula for the limiting energy current conjectured in [18] are correct. We then use this Green–Kubo type formula to investigate the relationship between the energy current and period of the forcing. This relationship is investigated in the case of significant rate of momentum flip, small rate of momentum flip and no momentum flip. We compare the relationship observed in the anharmonic case to that of the harmonic case for which explicit formulae are available [16].

We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter (varepsilon ) and converge weakly to a homogenized diffusion process in the limit (varepsilon rightarrow 0). In these results, we allow for the time horizon to blow up such that (T_varepsilon rightarrow infty ) as (varepsilon rightarrow 0). The novelty of the results arises from the circumstance that many quantities are unbounded for (varepsilon rightarrow 0), so that formerly established theory is not directly applicable here and a careful investigation of all relevant (varepsilon )-dependent terms is required. As a mathematical application, we then use these limit theorems to prove asymptotic properties of a minimum distance estimator for parameters in a homogenized diffusion equation.

We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of energy per degree of freedom. We extend this result to anharmonic perturbations with bounded second derivatives and boundary dissipation, proving that for small perturbations and non-resonant forcing, the dynamics converges to a periodic stationary state with energy exponentially localized uniformly in the system size. The perturbed periodic state is described by a convergent power type expansion in the strength of the anharmonicity. This excludes chaoticity induced by anharmonicity, independently of the size of the system. Our perturbative scheme can also be applied in higher dimensions.

The quantum thermodynamic performance of a Stirling cycle employing a three-spin Lipkin-Meshkov-Glick (LMG) model is investigated under varying magnetic interaction anisotropies and control parameters. The model operates in the anisotropic XY regime ((gamma =+1)), the Ising limit ((gamma =0)), and the mixed ferromagnetic regime ((gamma =-1)), with key thermodynamic quantities evaluated across a range of temperature ratios, magnetic field strengths, and coupling asymmetries. The mean energy landscape reveals a strong dependence on the anisotropy parameter, highlighting quantum coherence effects and spin alignment. The operational phase space is mapped, showing distinct transitions between heat engine, refrigerator, and heater modes, with (gamma =+1) exhibiting the broadest mode diversity and (gamma =-1) yielding robust engine-like behavior. Thermodynamic quantities such as heat exchange and work output are analyzed, showing mode transitions driven by magnetic field tuning. Efficiency, refrigeration performance (ε), and the refined performance coefficient (Π) are presented, revealing intricate dependencies on system parameters. Anisotropic spin coupling is shown to enhance thermodynamic responsiveness, while strong magnetic fields induce saturation and performance decline due to level polarization. The results demonstrated that quantum many-body interactions, when properly tuned, could be harnessed to optimize the design of nanoscale heat engines, refrigerators, and other quantum thermal devices.

We point out that area laws of quantum-information concepts indicate limitations of block transformations as well-behaved real-space renormalization group (RG) maps, which in turn guides the design of better RG schemes. Mutual-information area laws imply the difficulty of Kadanoff’s block-spin method in two dimensions (2D) or higher due to the growth of short-scale correlations among the spins on the boundary of a block. A leap to the tensor-network RG, in hindsight, follows the guidance of mutual information and is efficient in 2D, thanks to its mixture of quantum and classical perspectives and the saturation of entanglement entropy in 2D. In three dimensions (3D), however, entanglement grows according to the area law, posing a threat to a 3D block-tensor map as an apt RG transformation. As numerical evidence, we show that estimates of 3D Ising critical exponents fail to converge with respect to the RG step, making the 3D block-tensor map an unreliable RG method. Moreover, the estimates do not improve as more coupling constants are retained. As a guidance to proceed, a tensor-network toy model is proposed to capture the 3D entanglement-entropy area law.

In this contributions we consider the averaging principle and the large deviation principle of the stochastic reaction-diffusion system with fast oscillation and non-Lipschitz drift of any degree in unbounded channel-like domains. First, the well-posedness of solutions is established using a domain expansion method. Then, the averaging principle is proved, while we give a proof of unique ergodicity of frozen equation in the case of unbounded domains. Furthermore, we prove the large deviation principle based on the weak convergence method. Since the key property of compactness embeddings of the usual Sobolev spaces does not hold in our situation, we establish the uniform tail-end estimates to overcome the difficulties caused by the non-compactness embedding.

According to Verlinde’s conjecture(s), the gravitational interaction is just an emergent phenomenon of spatial variation of the entropy, generating the (r^{-2}) Newtonian force regardless of the distance scales. In this paper, the underlying arguments of such radial departure from distance scale are discussed in the framework of Boltzmann-Gibbs statistics for a gas composed of N quartic quantum anharmonic oscillators and exploiting an optimization procedure proposed by Burrows, Cohen, and Feldmann (BCF). The study in the framework of Boltzmann-Gibbs statistics is essential because it gives us a result that remains valid even at long-range interaction distances, contrary to what is said in the literature. We use the BCF optimization procedure to find low ((alpha ^*_textrm{low})) and high ((alpha ^*_textrm{high})) frequencies, the extremized partition function (Z_{alpha ^{*}}(beta )), the time evolution operator (mathcal {U}_{alpha ^*}(t,0)), and the density matrix (rho _{n,alpha ^*}) of the gas in a region where perturbation theory breaks down and it is no longer valid. After that, the expression of the ”original” partition function (Z_alpha (beta )) for such gas is obtained for both low and high frequencies. We prove that in the classical limit, (T rightarrow +infty ), the attempt fails, and one needs to modify the first conjecture to obtain the (r^{-2}) Newtonian force. In contrast, at the highest distances, (rgg 1), the second conjecture remains as it was postulated, but the gravity departs from its classical nature and exhibits (r^{-1}) MONDian force.