arXiv subjects

Jian-zu Zhang

Publications and source records attributed to Jian-zu Zhang.

15 recordsLinked to original sources

arXiv2004

Fractional Angular Momentum in Noncommutative Space

In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space-space noncommutativity and momentum-momentum noncommutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.

hep-th↗

arXiv2004

Testing Spatial Noncommutativity via Rydberg Atoms

The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic field, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads to that the canonical angular momentum possesses fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes $\hbar/2$. Furthermore, in the limit of eliminating magnetic field, the dominate value of the lowest canonical angular momentum changes from $\hbar/2$ to $\hbar/4$. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.

hep-ph↗

arXiv2004

Spectrum of q-Deformed Schrödinger Equation

The energy spectrum of q-deformed Schrödinger equation is demonstrated. This spectrum includes an exponential factor with new quantum numbers--the $q$-exciting number and the scaling index. The pattern of quark and lepton masses is qualitatively explained by such a q-deformed spectrum in a composite model.

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arXiv2003

A q-deformed Uncertainty Relation

Within the formulation of a q-deformed Quantum Mechanics a qualitative undercut of the q-deformed uncertainty relation from the Heisenberg uncertainty relation is revealed. When $q$ is some fixed value not equal to one, recovering of ordinary quantum mechanics and the corresponding recovering condition are discussed.

hep-th↗

arXiv2003

A q-deformed Quantum Mechanics

With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schrödinger equation are considered.

hep-th↗

arXiv2003

Structures of q-Deformed Currents

The non-perturbation and perturbation structures of the q-deformed probability currents are studied. According to two ways of realizing the q-deformed Heisenberg algebra by the undeformed operators, the perturbation structures of two q-deformed probability currents are explored in detail. Locally the structures of two perturbation q-deformed probability currents are different, one is explicitly potential dependent; the other is not. But their total contributions to the whole space are the same.

hep-th↗

arXiv2002

Perturbation Foundation of q-Deformed Dynamics

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one originates from the perturbation expansion of the potential in one configuration space, the other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved: (I) Equivalence theorem {\it I}: Perturbation expressions of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. (II) The general equivalence theorem {\it II}: for {\it any} potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied.

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arXiv2002

Testing Abelian dyon - fermion Bound System

Characteristics of Abelian dyon - fermion bound system, parity - violating effects, a new series of energy spectra, effects related to the non - vanishing electric dipole moment, feature of spin orientation etc, are analyzed and compared with hydrogen - like atom. These analyses explore possibility of a new approach of searching for dyons under bound condition.

hep-th↗

arXiv2002

q-Deformed Dynamics and Virial Theorem

In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.

hep-th↗

arXiv2001

Once again: Instanton method vs. WKB

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam${\acute e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.

hep-th↗

arXiv2001

Perturbative Equivalent Theorem in q-Deformed Dynamics

Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative expansion of the potential, the other originates from that of the kinetic energy term. At the level of operators, these two q-perturbative Hamiltonians are different. In order to establish a reliable foundation of the perturbative calculations in q-deformed dynamics, except examples of the harmonic-oscillator and the Morse potential demonstrated before, the general q-perturbative equivalent theorem is demonstrated, which states that for any regular potential which is singularity free the expectation values of two q-perturbative Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent. For the q-deformed ``free'' particle case, the perturbative Hamiltonian originated from the kinetic energy term still keeps its general expression, but it does not lead to energy shift.

hep-th↗

arXiv2001

Perturbative Aspects of q-Deformed Dynamics

Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schrödinger equation are analyzed. General representations of the additional momentum-dependent interaction originating from the q-deformed effects are presented in two approaches. As examples, such additional interactions related to the harmonic-oscillator potential and the Morse potential are demonstrated.

hep-th↗

arXiv2000

D-Branes and their Absorptivity in Born-Infeld Theory

Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.

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arXiv2000

Critical Phenomenon of a Consistent q-Deformed Squeezed State

Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special q-deformed squeezed states are constructed. Besides the similar local maximum squeezing as the one in the undeformed case, new strong squeezing appears when the amplitude of the related coherent state increases to large values. A critical phenomenon appears at a large value of the amplitude: the variance of one component of the quadrature of the light field approaches zero, but the variance of the corresponding conjugate quantity remains finite, which is a surprising deviation from Heisenberg's uncertainty relation. The qualitative character exposed by this q-squeezed state may provide some evidence about q-deformed effects in current experiments.

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arXiv1998

Higgs Production: CP Studies in e-e- Collisions

We review the production of scalar Higgs-like particles in high-energy electron-electron collisions, via the fusion of electroweak gauge bosons. The emphasis is on how to distinguish a CP-even from a CP-odd Higgs particle. Among the more significant differences, we find that in the CP-odd case, the Higgs spectrum is much harder, and the dependence of the total cross section on the product of the polarizations of the two beams is much stronger, than in the CP-even case. We also briefly discuss parity violation, and the production of charged Higgs bosons.

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