Related papers: Time Evolution of SU(1,1) coherent states
The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation.
In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
The Holstein-Primakoff representation for the su(2)-algebra is derived in the deformed boson scheme. The following two points are discussed : (i) connection between a simple Hamiltonian and the Hamiltonian obeying the su(2)-algebra such as…
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types…
We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
The issue of separating Schr\"odinger-type quantum time evolution into a product of holonomic and dynamical parts in the non-adiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible,…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…
Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that,…