Basics of Quantum Mechanics, Geometrization and Some Applications to Quantum Information
Reads0
Chats0
TLDR
A survey of the use of differential geometric formalisms to describe quantum mechanics can be found in this paper, where the authors analyze the Weyl-Wigner construction of quantum mechanics.Abstract:
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrodinger framework from this perspective and provide a description of the Weyl–Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses.read more
Citations
More filters
Journal ArticleDOI
Statistics and Nos\'e formalism for Ehrenfest dynamics
José L. Alonso,Andrea Castro,Jesús Clemente-Gallardo,J. C. Cuchí,Pablo Echenique,Fernando Falceto +5 more
TL;DR: In this article, the authors show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for EhrenFest dynamics.
Journal ArticleDOI
Statistics and Nosé formalism for Ehrenfest dynamics
José Luis Alonso,Andrea Castro,Jesús Clemente-Gallardo,J. C. Cuchí,Pablo Echenique,Fernando Falceto +5 more
TL;DR: In this article, the authors show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for EhrenFest dynamics.
Journal ArticleDOI
classical tensors and quantum entanglement i: pure states
TL;DR: In this paper, the authors consider the case when the immersed submanifold contains separable states or entangled states, and show that the Hermitian tensors can encode some properties of these states.
Journal ArticleDOI
Towards a definition of quantum integrability
TL;DR: In this article, the authors review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrabilities, and show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom.
Journal ArticleDOI
Geometry and symmetry of quantum and classical-quantum variational principles
Esther Bonet Luz,Cesare Tronci +1 more
TL;DR: In this article, the geometric setting of quantum variational principles was presented and extended to include the interaction between classical and quantum degrees of freedom, and the corresponding momentum map properties were presented as they arise from the underlying unitary symmetries.
References
More filters
Journal ArticleDOI
On the Quantum Correction For Thermodynamic Equilibrium
TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
Book ChapterDOI
On the quantum correction for thermodynamic equilibrium
TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
Journal ArticleDOI
Quantum mechanics as a statistical theory
TL;DR: In this article, an attempt is made to interpret quantum mechanics as a statistical theory, or more exactly as a form of non-deterministic statistical dynamics, which may hence be considered as an interpretation of quantum kinematics.
Journal ArticleDOI
Discussion of Probability Relations between Separated Systems
TL;DR: In this article, the probability relations which can occur between two separated physical systems are discussed, on the assumption that their state is known by a representative in common, and the two families of observables, relating to the first and to the second systems respectively, are linked by at least one match between two definite members.
Journal ArticleDOI
Making sense of non-Hermitian Hamiltonians
TL;DR: In this article, an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose + complex conjugate) is replaced by the physically transparent condition of space?time reflection ( ) symmetry.