Related papers: Generating Functionals for Harmonic Expectation Va…
Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in e.g.…
This study investigates the interplay between a high-frequency external forcing and the intrinsic dynamics of a quantum nonlinear parametric oscillator. To analyze this system, classical equations of motion of the averages of quantum…
Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion
Effective harmonic methods allow for calculating temperature dependent phonon frequencies by incorporating the anharmonic contributions into an effective harmonic Hamiltonian. The systematic errors arising from such an approximation are…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the…
We present first results on the calculation of fermionic spectral functions from analytically continued flow equations within the Functional Renormalization Group approach. Our method is based on the same analytic continuation from…
We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that…
We derive time dependent correlation functions in an one dimensional XY spin model with the use of generating functionals, the latter being defined as path integrals over fermionic coherent states. We focus on the proper construction of the…
In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
In this paper, we study generating functions for the standard orthogonal bases of spherical harmonics and spherical monogenics in R^m. Here spherical monogenics are polynomial solutions of the Dirac equation in R^m. In particular, we obtain…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
We present a method that permits the calculation of the dynamical correlation functions for quantum systems. These are obtained by evaluating the generating functionals of the static moments of the relaxation functions in a self-consistent…
We present the derivation of an alternative representation of the real-time in-in formalism under a spatially homogeneous and time independent electric field. Because the system exhibits instability associated with pair production of…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers…
In this paper, we study a family of generating functions whose coefficients are polynomials that enumerate partitions in lower order ideals of Young's lattice. Our main result is that this family satisfies a rational recursion and are…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
Firstly the fluctuation theorems (FT) for expended work in a driven nonequilibrium system, isolated or thermostatted, together with the ensuing Jarzynski work-energy (W-E) relationships, will be discussed and reobtained. Secondly, the…