相关论文: Coherent States and Duality

The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.

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…

An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for initial state with quantum coherence. In this paper, work statistics is considered from a fully new perspective of…

We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…

The generalized coherent states for quantum groups introduced by Jurco and Stovicek are studied for the simplest example SU_q(2) in full detail. It is shown that the normalized SU_q(2) coherent states enjoy the property of completeness, and…

Coherent states for equally spaced, homogeneous waveguide arrays are defined, in the infinite, semiinfinite and finite cases, and resolutions of the identity are constructed, using different methods. In the infinite case, which corresponds…

From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but…

Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the…

We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…

Coherent states have three main properties: coherence, overcompleteness and intrinsic geometrization. These unique properties play fundamental roles in field theory, especially, in the description of classical domains and quantum…

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…

The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…

Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear…

Quantum decoherence provides a framework to study the emergence of classicality from quantum systems by showing how interactions with the environment suppress interferences and select robust states known as pointer states. Earlier studies…

We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate…

Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…

We propose the notion of faithful coherent states based on the fidelity-based coherence witness. The criterion for detecting faithful coherent states can be restricted to a subclass of fidelity-based criterion under unitary transformations…

The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In…

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…