Probe Annihilation process on noncommutative spacetime
This paper has been withdrawn by Chien-Yu, Chen due to the authors fields error.
hep-ph↗
arXiv subjects
C. Y. Chen
Publications and source records attributed to C. Y. Chen.
Implementation of three-qubit Grover search in cavity QED
Using resonant interaction of three Rydberg atoms with a single-mode microwave cavity, we consider a realization of three-qubit Grover search algorithm in the presence of weak cavity decay, based on a previous idea for three-qubit quantum gate [Phys. Rev. A 73, 064304 (2006)]. We simulate the searching process under the influence of the cavity decay and show that our scheme could be achieved efficiently to find the marked state with high fidelity. The required operations are very close to the reach with current cavity QED techniques.
quant-ph↗
Counterexamples of Boltzmann's equation
To test kinetic theories, simple and practical setups are proposed. It turns out that these setups cannot be treated by Boltzmann's equation. An alternative method, called the path-integral approach, is then employed and a number of ready-for-verification results are obtained.
cond-mat.stat-mech↗
Nonexistence of time reversibility in statistical physics
Contrary to the customary thought prevailing for long, the time reversibility associated with beam-to-beam collisions does not really exist. Related facts and consequences are presented. The discussion, though involving simple mathematics and physics only, is well-related to the foundation of statistical theory.
cond-mat.stat-mech↗
Mathematical investigation of the Boltzmann collisional operator
Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more sophisticated than they appear to be.
physics.flu-dyn↗
A calculable and quasi-practical gas
A new kinetic approach is developed and a quasi-practical gas is defined to which the new approach can be applied. One of the advantages of this new approach over the standard one is direct calculability in terms of today's computational means.
cond-mat.stat-mech↗
Boltzmann's H-theorem and time irreversibility
It is shown that the justification of the Boltzman H-theorem needs more than just the assumption of molecular chaos and the picture of time irreversibility related to it should be reinvestigated.
physics.class-ph↗
Paradoxes in the Boltzmann kinetic theory
Paradoxes in the Boltzmann kinetic theory are presented. Firstly, it is pointed out that the usual notion concerning the perfect continuity of distribution function is not generally valid; in many important situations using certain types of discontinuous distribution functions is an absolute must. Secondly, it is revealed that there is no time reversibility in terms of beam-to-beam collisions and, in connection with this, there are intrinsic difficulties in formulating the net change of molecular density due to collisions, either in the three-dimensional velocity space or in the six-dimensional phase space. With help of simple examples, the paradoxes manifest themselves clearly.
physics.class-ph↗
Paradoxical aspects of the kinetic equations
Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples and direct analyses, involved paradoxes manifest themselves.
physics.flu-dyn↗
General procedure of solving the time-dependent Schrödinger equation
A nonperturbative procedure of solving the time-dependent Schrödinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that time-dependent systems become solvable (under the assumption that corresponding time-independent systems are solvable), the new approach unveils several misconcepts related to the usual wavefunction expansion and the standard perturbation theory.
quant-ph↗
A path-integral approach to the collisional Boltzmann gas
Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due to collisions, both the colliding molecules and the scattered molecules are allowed to have distributions; thus the calculation is done smoothly and no singularities arise.
physics.flu-dyn↗
A puzzle in quantum dynamics
The textbook treatment in that the wave function of a dynamical system is expanded in an eigenfunction series is investigated. With help of an elementary example and some mathematical theorems, it is revealed that in terms of solving the time-dependent Schrödinger equation the treatment involves in divergence trouble . The root reason behind the trouble is finally analyzed.
quant-ph↗
A path-integral approach to the collisionless Boltzmann gas
On contrary to the customary thought, the well-known ``lemma'' that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecule's path represents not the strength but the weakness of the standard theory. One of its consequences states that the velocity distribution at any point is a condensed ``image'' of all, complex and even discontinuous, structures of the entire spatial space. Admitting the inability to describe the entire space with a microscopic quantity, this paper introduces a new type of distribution function, called the solid-angle-average distribution function. With help of the new distribution function, the dynamical behavior of collisionless Boltzmann gas is formulated in terms of a set of integrals defined by molecular paths. In the new formalism, not only that the difficulties associated with the standard theory are surmounted but also that some of practical gases become calculable in terms of today's computer.
physics.data-an↗
Singularities in kinetic theory
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution functions involve a similar quasi-discontinuity difficulty.
physics.data-an↗
Time-dependent Perturbation Theory in Quantum Mechanics
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics of physical observables, instead of that of coefficients of wave-function expansion, is formulated so that the gauge-invariance and correspondence principles are observed naturally.
quant-ph↗
Microscopic discontinuity of fluids
We reveal that realistic fluids generate microscopic-level discontinuity constantly and the discontinuity spreads out with motion of particles rather rapidly and widely. These things cannot be treated by the standard kinetic equations, and thus the existing fluid theories, macroscopic ones and microscopic ones, need to be revised considerably.
physics.flu-dyn↗
Transition probability and preferential gauge
This paper is concerned with whether or not the preferential gauge can ensure the uniqueness and correctness of results obtained from the standard time-dependent perturbation theory, in which the transition probability is formulated in terms of matrix elements of Hamiltonian.
quant-ph↗
Vanishing spectral weight in a one-hole-doped antiferromagnet: A rigorous result
By explicitly tracking the Marshall sign, a phase string induced by hopping is revealed in the one-hole-doped $t-J$ model. It is rigorously shown that such a phase string cannot be eliminated through low-lying spin excitations, and it either causes the spectral weight $Z=0$, or leads to the localization of the doped hole. Implications for finite doping are also discussed.
cond-mat↗