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Families of superintegrable Hamiltonians constructed from exceptional polynomials
Families of superintegrable Hamiltonians exceptional polynomials Mathematical Physics
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
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
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...
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
multiple Charlier polynomials non-Hermitian Hamiltonians algebraic model
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
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
Hierarchy of integrable Hamiltonians nonlinear n-wave interaction Exactly Solvable and Integrable Systems
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
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...
Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems
Non-Hermitian Hamiltonians Studying Resonance Statistics
2010/12/27
We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systems
Marginality of bulk-edge correspondence for single-valley Hamiltonians
Marginality of bulk-edge correspondence single-valley Hamiltonians
2010/11/17
We study the correspondence between the non-trivial topological properties associated with the
individual valleys of gapped bilayer graphene (BLG), as a prototypical multi-valley system, and the gapl...
Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
Optical Lattice Hamiltonians Relativistic Quantum Electrodynamics
2011/1/14
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 ...
Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
post-Newtonian approximation binary and multiple stars celestial mechanics
2010/12/20
We derive the post-Newtonian next-to-leading order conservative spin-orbit and spin(a)-spin(b)
gravitational interaction Hamiltonians for arbitrary many compact objects. The spin-orbit Hamiltonian co...
Optical Lattice Hamiltonians for Relativistic Quantum Electrodynamics
Optical Lattice Hamiltonians Relativistic Quantum Electrodynamics
2010/11/24
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 ...
Supersymmetric extension of non-Hermitian su(2) Hamiltonians and supercoherent states
Pseudo-Hermitian quantum mechanics supersymmetry superco-herent states
2010/10/21
A new class of non-Hermitian Hamiltonians with real spectrum, which are writ-ten as a real linear combination of su(2) generators in the form H = !J3+ J−+ J+, 6= , is analyzed. The metric whic...
Ground states of unfrustrated spin Hamiltonians satisfy an area law
Ground states spin Hamiltonians area law
2010/10/20
We show that ground states of unfrustrated quantum spin-1=2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interact...
Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
Mapping Hamiltonians attractive repulsive potentials
2010/10/21
Through a simple and exact analytical derivation, we show that for a particle on a lattice, there is a one-to-one correspondence between the spectra in the presence of an attractive potential ˆ V...