Related papers: On quantization of nondispersive wave packets
We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations…
We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation.…
We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We present an ansatz for the initial conditions which leads to a unique determination of…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
A canonical quantization scheme is represented for a quantum system interacting with a nonlinear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of…
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
The canonical quantization of the essentially nonlinear midisuperspace model describing cylindrically symmetric gravitational waves with two polarizations is presented. A Fock space type representation is constructed. It is based on a…
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical…
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and…
The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now…
We consider BF-type topological field theory coupled to non-dynamical particle and string sources on spacetime manifolds of the form $\IR^1\times\MT$, where $\MT$ is a 3-manifold without boundary. Canonical quantization of the theory is…
We consider some modifications of the two dimensional canonical commutation relations, leading to {\em non commutative bosons} and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our…
In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum…
We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space $D=SU(m,1)/U(m)$, with the method of coherent state quantization. In the commutative limit we obtain the standard…
We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…