Related papers: Dynamical mapping method in nonrelativistic models…
In the paper we consider non-relativistic analog of the Nambu-Jona-Lasinio model and demonstrate, by this most simplified example, the method of dynamical mappings of Heisenberg fields on "physical" fields. We obtain the expressions for one…
Various exact solutions of two-particle eigenvalue problems for nonrelativistic contact four-fermion current-current interaction are obtained. Specifics of Goldstone mode is investigated. The connection between a renormalization procedure…
This thesis is devoted to studying aspects of real-time nonequilibrium dynamics in quantum field theory by implementing an initial value formulation of quantum field theory. The main focus is on the linear relaxation of mean fields and…
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix $A$. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to…
Two-dimensional Heisenberg antiferromagnets play a central role in quantum magnetism, yet the nature of dynamic correlations in these systems at finite temperature has remained poorly understood for decades. We solve this long-standing…
This paper is dedicated to formulate the interaction picture dynamics of the self-dual field minimally coupled to fermions. To make this possible, we start by quantizing the free self-dual model by means of the Dirac bracket quantization…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
The formal Heisenberg equations of the Federbush model are linearized and then are directly integrated applying the method of dynamical mappings. The fundamental role of two-dimensional free massless pseudo-scalar fields is revealed for…
Using the concept of dynamical mappings, two symmetry conserving nonperturbative approaches are presented. The first is based on the 1/N-expansion and sorted out using Holstein-Primakoff mapping. The second consists of dynamically mapping…
The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system under consideration extends the $1+1$ dimensional Heisenberg ferromagnet equation in…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schr\"odinger and in the Heisenberg representations. The role of Krein spaces is also discussed.
Working notes on setting up approximate dynamical systems and nonlinear eigenvalue problems, here embedded within the theory of complex nonlinear dynamics. Computations parallel those of linear quantum theory except that we use functional…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond.…
We show how to renormalize Phi-derivable approximations in a theory with a fermionic field coupled to a self-interacting scalar field through a Yukawa interaction. The nonperturbative renormalization concerns the self-interaction coupling…