Related papers: Relating the Lorentzian and exponential: Fermi's a…
Out of equilibrium quantum systems, on top of quantum fluctuations, display complex temporal patterns. Such time fluctuations are generically exponentially small in the system volume and can be therefore safely ignored in most of the cases.…
Fluctuation theorems have elevated the second law of thermodynamics to a statistical realm by establishing a connection between time-forward and time-reversal probabilities, providing invaluable insight into nonequilibrium dynamics. While…
Feynman's i-epsilon prescription for quantum field theoretic propagators has a quite natural reinterpretation in terms of a slight complex deformation of the Minkowski spacetime metric. Though originally a strictly flat-space result, once…
Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical…
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact,…
We show that the number of renewals up to time $t$ exhibits distributional fluctuations as $t\to\infty$ if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the…
The exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are founded, in the case when all working and repair times are bounded by exponential random…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
We study the behavior of the fermion propagator in an external time dependent potential in 0+1 dimension. We show that, when the potential has upto quadratic terms in time, the propagator can be expressed in terms of generalized Airy…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects…
In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving…
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature…
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional…
By using an exact analytical non-Hermitian approach in terms of resonance (quasinormal) states we express the decaying wave function as the sum of exponential and nonexponential decaying solutions to the time-dependent Schr\"odinger…
We review the theory of interacting Fermi systems whose low-energy physics is governed by forward scattering, i.e. scattering processes generated by effective interactions with small momentum transfers. These systems include Fermi liquids…
When a time propagator $e^{\delta t A}$ for duration $\delta t$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization…