相关论文: Geometric Phase and Classical-Quantum Corresponden…
We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy…
We elaborate on the distinction between geometric and dynamical phase in quantum theory and show that the former is intrinsically linked to the quantum mechanical probabilistic structure. In particular, we examine the appearance of the…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In…
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…
Since Pancharatnam's 1956 discovery of optical geometric phase, and Berry's 1984 discovery of geometric phase in quantum systems, researchers analyzing geometric phase have focused almost exclusively on algebraic approaches using the Jones…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We consider a quantum limit-cycle oscillator implemented in a spin system whose quantization axis is slowly rotated. Using a kinematic approach to define geometric phases in nonunitary evolution, we show that the quantum limit-cycle…
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the…
We calculate the geometric phase for an open system (spin-boson model) which interacts with an environment (ohmic or nonohmic) at arbitrary temperature. However there have been many assumptions about the time scale at which the geometric…
For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity…