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Standard derivations of the functional integral in non-equilibrium quantum field theory are based on the discrete time representation. In this work we derive the non-equilibrium functional integral for non-interacting bosons and fermions using a continuum time approach by accounting for the statistical distribution through the boundary conditions and using them to evaluate the Greens function.
In the setting of the principle of local equilibrium which asserts that the temperature is a function of the energy levels of the system, we exhibit plenty of steady states describing the condensation of free Bosons which are not in thermal equilibri
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group $U_q(mathcal L(m
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{alpha}(x), 0 leq x < infty, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g_{alpha}(x) suf
Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion and occurren
The theory of probability shows that, as the fraction $X_n/Yto 0$, the conditional probability for $X_n$, given $X_n+Y in h_{delta}:=[h, h+delta]$, has a limit law $f_{X_n}(x)e^{-psi_n(h_delta)x}$, where $psi_n(h_delta) $ equals to $[partial ln P(Y i