Related papers: Fock-space projection operators for semi-inclusive…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
New models of the Fock space sector corresponding to some fixed number of electrons are introduced. These models originate from the representability theory and their practical implementation may lead to essential reduction of dimensions of…
We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and…
Higher-order squeezing captures non-Gaussian features of quantum light by probing moments of the field beyond the variance, and is associated with operators involving nonlinear combinations of creation and annihilation operators. Here we…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
In this paper we define the Schwartz linear operators among spaces of tempered distributions. These operators are the analogous of linear continuous operators among separable Hilbert spaces, but in the case of spaces endowed with Schwartz…
We compute modular Hamiltonians for excited states obtained by perturbing the vacuum with a unitary operator. We use operator methods and work to first order in the strength of the perturbation. For the most part we divide space in half and…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
New effective operators, describing the photons with given polarization at given position with respect to a source are proposed. These operators can be used to construct the near and intermediate zones quantum optics. It is shown that the…
We give a construction of impurity operators in the `algebraic analysis' picture of RSOS models. Physically, these operators are half-infinite insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue of insertions of…
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…
The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined.…