Related papers: Evolution Operators for Linearly Polarized Two-Kil…
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.
The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators…
In this paper we provide a novel and general way to construct the result of the action of any bosonic or fermionic operator represented in second quantized form on a state vector, without resorting to the matrix representation of operators…
We revisit the non-perturbative renormalization of a class of simple polaron models with resting fermions. The considered dispersion relations and form factors are allowed to be highly singular, such that infinite self-energies and wave…
The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which $x\in\mathbb{R}$ and $t\in\mathbb{R}_+$. These equations contain…
In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary…
We investigate the complex time evolution of a vacuum state with the insertion of a local primary operator in two-dimensional conformal field theories (2d CFTs). This complex time evolution can be considered as a composite process…
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar…
The time-evolution operator obtained from the fractional-time Schr\"{o}dinger equation (FTSE) is said to be non-unitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We compute matrix elements of the evolution operator in the stochastic…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…