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Information geometry and the hydrodynamical formulation of quantum mechanics
Information geometry the hydrodynamical formulation quantum mechanics Differential Geometry
2012/4/18
Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M.
The Universal Arrow of Time II: Quantum mechanics case
Quantum mechanics The Universal Arrow of Time chaotic macroscopic systems classical Hamilton mechanics
2011/7/7
The given paper is natural continuation of our previous paper arXiv:1011.4173 We have illustrated earlier, that in the classical Hamilton mechanics for an overwhelming majority of real chaotic macrosc...
Nonlinear Boundaries in Quantum Mechanics
Nonlinear Boundaries Quantum Mechanics quantum eigenvalue equations gauge invariant
2011/7/7
Based on empirical evidence, quantum eigenvalue equations appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimens...
Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics
Dirac Operator Complex Manifolds Supersymmetric Quantum Mechanics
2011/3/2
We explore a new simple N = 2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holom...
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/2/24
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
Fuzzy Scalar Field Theory as Matrix Quantum Mechanics
Fuzzy Scalar Field Theory Matrix Quantum Mechanics
2011/3/3
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix mo...
A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics
Closed Formula Barrier Transmission Coefficient Quaternionic Quantum mechanics
2011/2/24
A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics.
Supersymmetric quantum mechanics and Painleve IV equation
Supersymmetric quantum mechanics Painleve IV equation
2011/1/17
It will be seen that the determination of general one-dimensional Schr¨odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev´e IV equation. It shall...
Riemann hypothesis and Quantum Mechanics
Bost-Connes model Riemann Hypothesis Primorial numbers
2011/3/4
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
Applications of density matrix in the fractional quantum mechanics
Applications of density matrix fractional quantum mechanics
2011/2/25
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. W...
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...
Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type
Extended Supersymmetric Quantum Mechanics Fierz Schur Type
2011/1/18
We discuss two independent constructions to introduce an N-extended Super-symmetric Quantum Mechanics. The first one makes use of the Fierz identities while the second one (divided into two subcases) ...
Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory
Modal Hamiltonian interpretation of quantum mechanics Casimir operators quantum field theory
2011/3/2
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.
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...
The Clifford Algebra approach to Quantum Mechanics A: The Schroedinger and Pauli Particles
The Clifford Algebra approach Quantum Mechanics
2010/11/23
In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to a...