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The spherical Sherrington-Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy-Widom at low temperature.…
A sweep through a quantum phase transition by means of a time-dependent external parameter (e.g., pressure) entails non-equilibrium phenomena associated with a break-down of adiabaticity: At the critical point, the energy gap vanishes and…
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism has changed. This work is concerned with open-end,…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims…
We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
We consider the scenario of a fluctuating spacetime due to a deformed commutation relation with a fluctuating deformation parameter, or to a fluctuating metric tensor. By computing the resulting dynamics and averaging over these…
While the warming trends of the Earth's mean temperature are evident at climatological scales, the local temperature at shorter timescales are highly fluctuating. In this letter we show that the probabilities of such fluctuations are…
We propose a Bayesian hierarchical model to simultaneously estimate mean based changepoints in spatially correlated functional time series. Unlike previous methods that assume a shared changepoint at all spatial locations or ignore spatial…
We consider a quantum harmonic oscillator coupled to a general nonequilibrium environment. We show that the decoherence factor can be expressed in terms of a measurable effective temperature, defined via a generalized…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
The high temperature limit of interacting spins is usually not associated with ordering or critical phenomena. Nevertheless, spontaneous fluctuations of a local spin polarization at equilibrium have nontrivial dynamics even in this limit.…
We investigate thermal effects on density fluctuations in confined classical liquids using phonon quantization. The system is modeled via a massless scalar field between perfectly reflecting parallel planes with Dirichlet, Neumann, and…
Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
Biologically driven non-equilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures…
We experimentally test the Crooks fluctuation theorem in a quantum spin system. Our results show that the Crooks fluctuation theorem is valid for different speeds of the nonequilibrium processes and under various effective temperatures.…
Quantum coherences characterise the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems these coherences can fluctuate. A simple toy model to study such…