Related papers: Classical and quantum resonances for hyperbolic su…
On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an…
Classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate $\hbar$-independent quantum canonical maps. It is shown that such maps act in the…
We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including…
Given a closed orientable hyperbolic manifold of dimension $\neq 3$ we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold.…
In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve $(X, \sigma_X)$, where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or…
The phenomenon of Parametric Resonance (PR) is very well studied in classical systems with one of the textbook examples being the stabilization of a Kapitza's pendulum in the inverted configuration when the suspension point is oscillated…
The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic…
Chern number formulas for holomorphic jet bundles are computed for projective curves and for projective surfaces. These formulas are used to show that certain minimal surfaces of general type (generic hypersurfaces of degree at least 5 in…
In this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states…
The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there…
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…