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Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom
fast diffusion non-convex Hamiltonians two degrees of freedom
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2015/9/25
In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees offreedom, and we prove a result of diffusion for an open and dense set of perturbations, ...
Families of superintegrable Hamiltonians constructed from exceptional polynomials
Families of superintegrable Hamiltonians exceptional polynomials Mathematical Physics
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2012/6/19
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum t...
Resolutions of identity for some non-Hermitian Hamiltonians II: proofs
non-Hermitian quantum mechanics exceptional points resolution of identity
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2011/9/23
Abstract: This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated func...
Resolutions of identity for some non-Hermitian Hamiltonians I: exceptional point in continuous spectrum
non-Hermitian quantum mechanics exceptional points resolution of identity
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2011/9/23
Abstract: Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entir...
Connecting orbits for families of Tonelli Hamiltonians
families of Tonelli Hamiltonians Dynamical Systems
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2011/9/19
Abstract: We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the flows of a family of Tonelli Hamiltonians. Our approach is close to the one of...
Creation of Homoclinic Tangencies in Hamiltonians by the Suspension of Poincaré Sections
Hamiltonian vector field Anosov flow elliptic point homoclinic tangency
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2011/9/16
Abstract: In this note we show that for any Hamiltonian defined on a symplectic 4-manifold M and any point p in M, there exists a C2-close Hamiltonian whose regular energy surface through p is either ...
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
multiple Charlier polynomials non-Hermitian Hamiltonians algebraic model
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2011/7/26
Abstract: A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of mult...
Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling
Integrable relativistic systems Hamiltonians momentum-spin-orbit coupling
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2011/7/26
Abstract: In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We inte...
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
nonlinear n-wave Hamiltonians Hierarchy
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2011/7/7
In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltoni...
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
Hierarchy of integrable Hamiltonians nonlinear n-wave interaction Exactly Solvable and Integrable Systems
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2011/7/26
Abstract: In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special...
Ground states of semi-relativistic Pauli-Fierz and no-pair Hamiltonians in QED at critical Coulomb coupling
Existence of ground states exponential localization no-pair Hamiltonian quantum electrodynamics
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2011/7/26
Abstract: We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulo...
Metric operators for non-Hermitian quadratic su(2) Hamiltonians
Metric operators non-Hermitian quadratic su(2) Hamiltonians
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2011/3/1
A class of non-Hermitian quadratic su(2) Hamiltonians that ful l an anti-linear symmetry is constructed. If unbroken this anti-linear symmetry leads to a purely real spectrum and the Hamiltonian can b...
Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems
Non-Hermitian Hamiltonians Studying Resonance Statistics
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2010/12/27
We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systems
Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
Optical Lattice Hamiltonians Relativistic Quantum Electrodynamics
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2011/1/7
We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on la...
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
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2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...