Gluon transport equations,plasma oscillations,and screening

The gluon transport equations (Phys. Lett. 177B (1986) 402) are reconsidered to derive a consistent semiclassical limit. Introducing the color current of gluon fluctuations around a classical mean field, we calculate the color permeability function of a collisionless gluon plasma in linear response approximation. The dispersion relations and electric screening length agree with one-loop high temperature QCD results. We find no magnetic screening atO(g ²) and predict transverse magnetic plasma oscillations similar to electric ones. The extension to include particle production by a mean color field is shortly described.     

Equal-time kinetic equations in a rotational field

We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in rotating frame we derive the complete set of kinetic equations for the spin components of the 8- and 7-dimensional Wigner functions. While the particles are no longer on a mass shell in the general case due to the rotation–spin coupling, there are always only two independent components, which can be taken as the number and spin densities. With help from the off-shell constraint we obtain the closed transport equations for the two independent components in the classical limit and at the quantum level. The classical rotation–orbital coupling controls the dynamical evolution of the number density, but the quantum rotation–spin coupling explicitly changes the spin density.     

Breakdown of universality in quantum chaotic transport: the two-phase dynamical fluid model

We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic classical dynamics, and result from the separation of the quantum phase space into a stochastic and a deterministic phase. Consequently, sample-to-sample conductance fluctuations lose their universality, while the persistence of a finite stochastic phase protects the universality of conductance fluctuations under variation of a quantum parameter.     

Classical and quantum transport through entropic barriers modeled by hardwall hyperboloidal constrictions

We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrödinger equation and the classical equations of motion for these geometries, we study in detail the quantum transmission probabilities and the associated quantum resonances, and relate them to the classical phase structures which govern the transport through the constrictions. These classical phase structures are compared to the analogous structures which, as has been shown only recently, govern reaction type dynamics in smooth systems. Although the systems studied in this paper are special due their separability they can be taken as a guide to study entropic barriers resulting from constriction geometries that lead to non-separable dynamics.     

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.     

Quantum theory of the Hall effect

We discuss a model of both the classical and the integer quantum Hall effect which is based on a semiclassical Schrödinger-Chern-Simons action, where the Ohm equations result as equations of motion. The quantization of the classical Chern-Simons part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall effect is described by a theory which arises as the classical limit of a theory of the quantum Hall effect. The model also explains the preference and the domain of the edge currents on the boundary of samples.     

Gluon Transport Properties in the Region of Coexistence of Both Hadronic and QGP Phases

The transport properties of gluon in color space in a system of coexistence of both hadronic and QGP phases are investigated from the quantum transport equation of gluon.     

Classical limit of relativistic quantum mechanical equations in the Foldy-Wouthuysen representation

It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen (FW) representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the replacement of operators in the Hamiltonian and quantum mechanical equations of motion by the respective classical quantities.     

The Quantum-Classical Comparison of the Arrival-Time Distribution Through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.     

A Hybrid Kinetic-Quantum Model for Stationary Electron Transport

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schrödinger equations are presented in the one-dimensional stationary setting. These interface conditions, derived thanks to an asymptotic analysis of the Wigner transform, are shown to be flux-preserving and are used to build a hybrid model consisting of a quantum zone surrounded by two classical ones. The hybrid model is shown to be well posed when the potential is either prescribed or computed self-consistently, and the semiclassical limit of the problem is shown to give the right interface conditions between two kinetic regions (the electrostatic potential being fixed). This model can be used to describe far-from-equilibrium electron transport in a resonant tunneling diode.     

Self-energy of heavy quark

We demonstrate that to calculate the selfenergy of a heavy quark in the heavy quark limit (or the heavy fermion limit in what is called the Baryon Chiral Perturbation Theory), the use of standard dimensional regularization provides only the quantum limit: opposite to the heavy quark (or classical) limit that one wishes to obtain. We thus devised a standard ultraviolet/infrared regularization procedure in calculating the one- and two-loop contributions to the heavy quark self-energy in this limit. Then the one-loop result is shown to provide the standard classical Coulomb self-energy of a static colour source that is linearly proportional to the ultraviolet cutoff Λ. All the two-loop contributions are found to be proportional to Λ In (Λ/γ) where γ is the infrared cutoff. Often only the contribution from the bubble (light quarks, gluon and ghost) insertion to the gluon propagator has been considered as theO(α _s ) correction to the Coulomb energy to this order. Our result shows that other contributions are of the same magnitude, thus have to be taken into account.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.     

Open quantum dots: II. Probing the classical to quantum transition

Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review?(Ferry et?al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.     

Radiative reaction and quantum mechanics

According to the principles of quantum mechanics, the classical Lorentz-Dirac equations of the electron should follow from quantum electrodynamics in the classical limit. We show this is indeed true for the special case in which the charge does not radiate, provided the momentum operators in the Dirac theory are identified, in the classical limit, with the effective momenta of the Lorentz-Dirac equations.     

Regge behaviour of distribution functions and t and x-evolutions of gluon distribution function at low-x

In this paper, t and x-evolutions of gluon distribution function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in leading order (LO) at low-x are presented assuming the Regge behaviour of quarks and gluons at this limit. We compare our results of gluon distribution function with MRST 2001, MRST 2004 and GRV 1998 parametrizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-x. We also discuss the limitations of Taylor series expansion method used earlier to solve DGLAP evolution equations in the Regge behaviour of distribution functions.      

A causal quantum theory in phase space

The causal theory for the coherent state representation of quantum mechanics is derived. The general conditions for the classical limit are given and it is shown that phase space classical mechanics can be obtained as a limit even for stationary states, in contrast to the de Broglie-Bohm quantum theory of motion.     

Dirac方程中的量子与经典对应

根据Heisenberg对应原理(HCP),在经典极限下厄密算符的量子矩阵元对应经典物理量的Fourier展开系数.将HCP应用到相对论领域的Dirac方程中,对于自由粒子和在匀磁场中的带电粒子,其量子算符的矩阵元在经典极限下对应着相对论物理方程的解.计算表明,在经典极限下量子期望值就是对应经典物理量的时间平均值.