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Chang-Pu Sun

Publications and source records attributed to Chang-Pu Sun.

44 records · Page 3Linked to original sources
arXiv1994

Quantum Dynamical Approach of Wavefunction Collapse in Measurement Process and Its Application to Quantum Zeno Effect

The systematical studies on the dynamical approach of wavefunction collapse in quantum measurement are reported in this paper based on the Hepp-Coleman's model and its generalizations. Under certain physically reasonable conditions, which are easily satisfied by the practical problems, it is shown that the off-diagonal elements of the reduced density matrix vanish in quantum mechanical evolution process in the macroscopic limit with a very large particle number N. Various examples with detector made up of oscillators of different spectrum distribution are used to illustrate this observations . With the two-level system as an explicit illustration, the quantum information entropy is exactly obtained to quantitatively describe the degree of decoherence for the so-called partial coherence caused by detector. The entropy for the case with many levels is computed based on perturbation method in the limits with very large and very small N. As an application of this general approach for quantum measurement, a dynamical realization of the quantum Zeno effect are present to analyse its recent testing experiment in connection with a description of transition in quantum information entropy. Finally, the Cini's model for the correlation between the states of the measured system and the detector is generalized for the case with many energy-level.

hep-th↗
arXiv1993

Wave Function Evolution of a Dissipative System

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.

hep-th↗
arXiv1993

High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.

hep-th↗
arXiv1993

Quantum Dynamical Model for Wave Function Reduction in Classical and Macroscopic Limits

In this papper, a quantum dynamical model describing the quantum measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and macroscopic limit with very large particle number in measuring instrument, this model generally realizes the wave packet collapse in quantum measurement as a consequence of the Schrodinger time evolution in either the exactly-solvable case or the non-(exactly-)solvable case. For the latter, its quasi-adiabatic case is explicitly analysed by making use of the high-order adiabatic approximation method and then manifests the wave packet collapse as well as the exactly-solvable case. By highlighting these analysis, it is finally found that an essence of the dynamical model of wave packet collapse is the factorization of the Schrodinger evolution other than the exact solvability. So many dynamical models including the well-known ones before, which are exactly-solvable or not, can be shown only to be the concrete realizations of this factorizability

hep-th↗
arXiv1992

Exotic Quantum Double,Its Universal R-matrix And Their Representations

The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld's quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum doubles that are the q-deformations for Lie algebras or Lie superalgebras. By studying its representation theory,many-parameter representations of the exotic quantum double are obtained with an explicit example associated with Lie algebra $A_2$ .The multi-parameter R-matrices for the quantum Yang-Baxter equation can result from the universal R-matrix of this exotic quantum double and these representattions.

hep-th↗
arXiv1992

The Canonical Quantization in Terms of Quantum Group and Yang-Baxter Equation

In this paper it is shown that a quantum observable algebra, the Heisenberg-Weyl algebra, is just given as the Hopf algebraic dual to the classical observable algebra over classical phase space and the Plank constant is included in this scheme of quantization as a compatible parameter living in the quantum double theory.In this sense,the quantum Yang-Baxter equation naturally appears as a necessary condition to be satisfied by a canonical elements,the universal R-matrix,intertweening the quantum and classical observable algebras. As a byproduct,a new ``quantum group'' is obtained as the quantum double of the classical observable algebra

hep-th↗
arXiv1992

The l-State Boson Algebra as a Non-Standard Quantum Double and its Universal R-Matrix for Yang-Baxer Equation

In this paper we construct a new quantum double by endowing the l-state bosonalgebra with a non-trivial Hopf algebra structure,which is not a q-deformation of the Lie algebra or superalgebra.The universal R-matrix for the Yang-Baxter equation associated with this new quantum group structure is obtained explicitly.By building the representations of this quantum double,we get some R-matrices ,which can result in new representations of the braid group.

hep-th↗