We analyze the limiting dynamics of two copies of a disordered mean-field spherical $p$-spin system coupled non-reciprocally to one another and initialized independently of the disorder. We prove that, on every finite time interval, as the system size tends to infinity, the empirical correlation and integrated response functions converge almost surely and in $L^q$ for $q \geq 1$, uniformly in time, to the unique non-random solution of a system of coupled integro-differential equations. For even $p$-spin models, we establish stationarity and exponential decay of the correlation and response functions in the high-temperature regime. In the special case of the spherical Sherrington--Kirkpatrick model, we derive explicit representations of the limiting correlation and integrated response functions. These representations allow us to characterize the long-time dynamics throughout the full range of temperatures. In particular, we prove the occurrence of aging in the low-temperature regime and fluctuation-dissipation behavior in the high-temperature regime, and provide a separate characterization of the dynamics at the critical temperature.
For chaotic many-body systems as well as the random energy model, the logarithm of the (scaled) spectral form factor (SFF) exhibits two robust properties at late times: (i) self-averaging and (ii) a reflected-Gumbel distribution. Here, we demonstrate that both properties break down for $N$ non-interacting fermions on a...
Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per s...
Igor Timofeev, D. Hryniuk, Marzena H. Szymańska· 0 citations
We propose a novel framework for analyzing the sample-path large deviations of interacting particle systems directly on a lattice by considering a large-spin limit ($s \to \infty$). Through an appropriate scaling of variables, the process concentrates around its deterministic trajectory, governed by the lattice diffusi...
It has been shown that Discrete Time Crystal (DTC) behavior may arise in the periodically driven, open Dicke model in the thermodynamic limit ($N \rightarrow \infty$). In this work, we demonstrate that finite $N$ non-mean-field fluctuations in this model can lead to decay rates and amplitudes of transient DTCs that dis...
We investigate the statistical mechanics of a system coupled to multiple heat reservoirs at different temperatures, a setting which typically sustains nontrivial circulation. By applying a canonical transformation, we map the system onto that of a particle coupled to a single reservoir yet driven by a deterministic cur...
We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for extendi...
Kai-Hsin Wu, A. Sandvik, Y. Kao· 0 citations
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