Coordinate-momentum Space Research Articles

Photon polarization tensor in a magnetized plasma: Absorptive part

We calculate the absorptive part of the photon polarization tensor in a hot magnetized relativistic plasma. In the derivation, we utilize a Landau-level representation for the fermion Green's function in a mixed coordinate-momentum space and obtain a closed-form expression for the one-loop polarization tensor. At the leading order in the coupling, its absorptive part is determined by particle and antiparticle splitting processes ($e^{-} \leftrightarrow e^{-}+\gamma$ and $e^{+} \leftrightarrow e^{+}+\gamma $, respectively), as well as by particle-antiparticle annihilation processes ($e^{-} + e^{+}\leftrightarrow \gamma$). The interpretation in terms of quantum transitions between Landau levels is also given. By making use of the photon polarization tensor, we study the differential photon emission rate in the quantum limit of magnetized relativistic plasma. At low energies, the photon emission has a prolate profile with the symmetry axis along the line of the magnetic field. At high energies, on the other hand, the photon emission has an oblate profile. The underlying reasons for such emission profiles are given in both regimes. The general result for the photon polarization tensor is also used to calculate the longitudinal and transverse components of magneto-optical conductivity.

Phase-space distribution functions for photon propagation in waveguides coupled to a qubit

We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that the distribution function of the transmitted pulse can be negative for the nonclassical input (i.e., single-photon Fock state). This reveals the quasiprobability nature of photon distribution. Analytical expressions for photon densities in the momentum space as well as in the coordinate space are obtained for the mentioned single-photon Gaussian input. We also study evolution of the multimode coherent-state input for an arbitrary photon number. Time-dependent differential equations describing average densities and fluctuations of outgoing photons are derived and solved. Influence of the number of input photons, pulse width, and radiation-atom interaction strength on the statistical properties of the fluctuations is investigated.

Path integral approach to eikonal and next-to-eikonal exponentiation

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

A Quantum Theory of Thermodynamic Relaxation

A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution.

General approach to functional forms for the exponential quadratic operators in coordinate-momentum space

In a recent paper (Nieto M M 1996 Quantum Semiclass. Opt. 8 1061, quant-ph/9605032), the one-dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering the multidimensional exponential quadratic operator (EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single-mode and double-mode EQO through the squeezed operator and the time-displacement operator of the harmonic oscillator.

Dephasing maps for quantum stochastic systems

Stochastic time evolution in a nonseparable and nonintegrable quantum system is manifested by rapid dephasing of gaussian wavepackets, whose topological distribution in the coordinate-momentum space defines its irregular regions, while wavepackets initiated in regular regions exhibit quasiperiodic evolution. A gradual transition from quasiperiodic to chaotic dynamics with increasing energy is observed.

Towards a theory of linear nonequilibrium statistical mechanics

A unified and comprehensive presentation is given of a treatment suitable for the description, in terms of classical statistical mechanics, of the approach to thermodynamic equilibrium of an ensemble of systems displaced macroscopically from equilibrium. The method apes, as far as possible, the Gibbs treatment of equilibrium ensembles. The selection of thermodynamic variables that fluctuage independently, chosen so that the second derivatives of the entropy are diagonal and normalized, correspond to functions in the coordinate momentum space (gamma space) that are normalized and mutually orthogonal. A further (unitary) transformation diagonalizes the Onsager Matrix connecting thermodynamic flux and displacement forces. The probability density in phase space describing an ensemble of systems displaced by a sinusoidal unit amplitude from equilibrium along one such thermodynamic variable can be described as the equilibrium function times unity plus a displacement function. These displacement functions are normalized and mutually orthogonal. Their decay with time are independent and can be analyzed in terms of spectral functions giving the amplitudes of eigenfunctions of the Liouville operator which compose them.