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We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
In this article we consider a path integral formulation of the Hubbard model based on a SU(2)-symmetrical Hubbard-Stratonovich transformation that couples auxiliary field to the local electronic density. This decoupling is known to have a…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
Instantons are tunneling solutions that connect two vacua, and under a small change in the potential, instantons sometimes disappear. We classify these disappearances as smooth (decay rate goes to 0 at disappearance) or abrupt (decay rate…
The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are…
We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator…
I illustrate the phenomenological application of Dyson-Schwinger equations to the calculation of meson properties observable at TJNAF. Particular emphasis is given to this framework's ability to unify long-range effects constrained by…
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial…
We give series solutions to single insertion place propagator-type systems of Dyson--Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a…
We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents $\zeta_n$ of the structure functions $S_n$ for $n\gg1$ under the additional condition…
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
We consider winding number transitions in the two dimensional O(3) non-linear sigma model, modified by a suitable conformal symmetry breaking term. We discuss the general properties of the relevant instanton solutions which dominate the…
We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional K\"ahler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in…
We study one-dimensional stochastic differential equations of form $dX_t = \sigma(X_t)dY_t$, where $Y$ is a suitable H\"older continuous driver such as the fractional Brownian motion $B^H$ with $H>\frac12$. The innovative aspect of the…
In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in [15, 16, 24], namely existence when the so called TT-tensor…
The Schwinger model, defined in the space interval $-L \le x \le L$, with (anti)periodic boundary conditions, is canonically quantized in the light-cone gauge $A_-=0$ by means of equal-time (anti)commutation relations. The transformation…
We consider invariant matrix models with log-normal (asymptotic) weight. It is known that their eigenvalue distribution is intermediate between Wigner-Dyson and Poissonian, which candidates these models for describing a system intermediate…
We study the nonlinear Schr$\ddot{o}$dinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized…
A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the…