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A FAST SPECTRAL ALGORITHM FOR THE QUANTUM BOLTZMANN COLLISION OPERATOR
Quantum Boltzmann equation fast spectral method
2015/7/14
This paper introduces a fast spectral algorithm for the quantum Boltzmann collision operator. In the usual spectral framework, one of the terms in the operator cannot be evaluatedefficiently. The new ...
The quantum scattering limit for a regularized Wigner equation
quantum scattering limit regularized Wigner equation
2015/7/14
We consider a regularized Wigner equation with an oscillatory kernel, the regularization acts in the space variable to damp high frequencies. The oscillatory kernel is directly derived from the Schrod...
The role of Chern Simons theory in solving the fractional quantum Hall effect mystery
Chern Simons theory fractional quantum Hall effect
2015/3/19
The role of Chern Simons theory in solving the fractional quantum Hall effect mystery.
D-bar and Dirac Type Operators on Classical and Quantum Domains
Dirac Operators Noncommutative Geometry
2015/1/19
I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the in...
From quantum $A_N$ (Calogero) to $H_4$ (rational) model
quantum Calogero rational model quasi exactly solvable quantum models
2011/7/7
A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them are characterized by...
Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
Quadratic Algebra Relativistic Quantum Smorodinsky-Winternitz Systems
2011/1/19
There exist a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude (SVPEM) and the Schrödinger equation.
The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolum...
On a nonlinear problem intervening in relativistic quantum mechanics perturbed by a factor of amortizement
nonlinear hyperbolic problem perturbed amortizement
2010/9/25
In this work, we study the existence and the uniqueness and the regularity of the solution of a problem governed by a nonlinear equation intervening in relativistic quantum mechanics perturbed by an a...
Asymptotic entanglement in 1D quantum walks with a time-dependent coined
Asymptotic entanglement 1D quantum walks time-dependent coined
2011/3/3
In this paper we investigate the asymptotic behavior of coin position entanglement (CPE) of a discrete-time quantum walk in one dimensional lattice using a time-dependent unitary coin operator.
Quantum Boolean Algebras
Quantum Boolean Algebras math
2010/11/24
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
L'Hopital-Type Rules Quantum Calculus
2010/11/24
We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give some new upper and lo...
The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach
The Clifford Algebra Quantum Mechanics
2010/11/23
In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to constr...
Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf su...
The quantum $H_4$ integrable system is a $4D$ system with rational potential related to the non-crystallographic root system $H_4$ with 600-cell symmetry. It is shown that the gauge-rotated $H_4$ Hami...