Related papers: Unitary Evolution on a Phase Space with Power of T…
This paper is concerned with the quantum theory of noncommutative scalar fields in two dimensional space time. It is shown that the noncommutativity originates from the the deformation of symplectic structures. The quantization is performed…
A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…
We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…
We introduce coordinates on the spaces of framed and decorated representations of the fundamental group of a surface with nonempty boundary into the symplectic group $Sp(2n,\mathbf R)$. These coordinates provide a noncommutative…
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…
Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties. Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates. This paper is concerned…
In the studies of the squeezing it is customary to focus more attention on the particular squeezed states and their evolution than on the dynamical operations that could squeeze simultaneously some wider families of quantum states,…
We develop a new method of representation of quantum states in terms of the displaced number states. We call it representation, where is an amplitude of the base displaced states. In particular, representation was obtained for set of the…
In this paper we analyze the evolution of the time averaged energy densities associated with a family of solutions to a Schr{\"o}dinger equation on a Lie group of Heisenberg type. We use a semi-classical approach adapted to the stratified…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic…
A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept.…