Long-range correlations in Boltzmann-Langevin model

The average phase-space density described by the Boltzmann-Langevin model can largely deviate from the one provided by the Boltzmann-Uhling-Uhlenbeck model, due to the non-linear evolution of density fluctuations. This aspect is investigated for long-wavelength, small density fluctuations in the framework of a memory incorporated Boltzmann-Langevin model. It is shown that the correlations associated with density fluctuations yield a collision term describing coupling between the collective vibrations and the single-particle degrees of freedom, which may play an important role in damping of collective motion in both the stable and unstable regions.     

Quantum interference and statistical fluctuations in deep-inelastic heavy-ion reactions

Starting from the general multi-channel formulation of the scattering matrix we perform a coarse-grain average of the cross section appropriate for the observed quantities in heavy-ion reactions. We keep full track of the geometrical factors for the coupling of partial waves and channel spin. Relating the diagonal part of the S-matrix product semiclassically to the statistical treatment in terms of phase-space trajectories we are dealing with quantum fluctuations and statistical fluctuations on an even basis. Quantum corrections play a minor role if the underlying statistical model takes effects of the nonthermalized relative motion properly into account. This is true even for small energy losses.     

Anomalous Fluctuations in the Motion of Partitioning Objects

We study how an object that partitions in two its thermally agitated environment relaxes to its equilibrium fluctuations. Event-driven molecular dynamics indicate that a conventional diffusive-like bound-Brownian motion is reached after a long-lived sub-diffusive regime. The two-stage behavior is not eliminated increasing the number of agitated particles, suggesting that the origin of the effect is a topologically frustrated exploration of phase-space.     

Observation of nonlinear frequency-sweeping suppression with rf diffusion

Nonlinear frequency sweeping of unstable waves in a laboratory plasma is suppressed upon application of rf fields. Frequency sweeping is driven by a population of energetic electrons trapped in a magnetic dipole field that excite drift-resonant potential fluctuations and create coherent structures in phase space. Self-consistent numerical simulation reproduces the suppression and suggests an explanation due to rf scattering of energetic electrons that destroys the phase-space structures.     

Causal signal transmission by quantum fields. V: Generalised Keldysh rotations and electromagnetic response of the Dirac sea

The connection between real-time quantum field theory (RTQFT) [see, e.g., A. Kamenev and A. Levchenko, Adv. Phys. 58 (2009) 197] and phase-space techniques [E. Wolf and L. Mandel, Optical Coherence and Quantum Optics (Cambridge, 1995)] is investigated. The Keldysh rotation that forms the basis of RTQFT is shown to be a phase-space mapping of the quantum system based on the symmetric (Weyl) ordering. Following this observation, we define generalised Keldysh rotations based on the class of operator orderings introduced by Cahill and Glauber [K.E. Cahill, R.J. Glauber, Phys. Rev. 177 (1969) 1882]. Each rotation is a phase-space mapping, generalising the corresponding ordering from free to interacting fields. In particular, response transformation [L.I. Plimak, S. Stenholm, Ann. Phys. (N.Y.) 323 (2008) 1989] extends the normal ordering of free-field operators to the time-normal ordering of Heisenberg operators. Structural properties of the response transformation, such as its association with the nonlinear quantum response problem and the related causality properties, hold for all generalised Keldysh rotations.Furthermore, we argue that response transformation is especially suited for RTQFT formulation of spatial, in particular, relativistic, problems, because it extends cancellation of zero-point fluctuations, characteristic of the normal ordering, to interacting fields. As an example, we consider quantised electromagnetic field in the Dirac sea. In the time-normally-ordered representation, dynamics of the field looks essentially classical (fields radiated by currents), without any contribution from zero-point fluctuations. For comparison, we calculate zero-point fluctuations of the interacting electromagnetic field under orderings other than time-normal. The resulting expression is physically inconsistent: it does not obey the Lorentz condition, nor Maxwell’s equations.     

Operational Phase-Space Probability Distribution in Quantum Communication Theory

Operational phase-space probability distributions are useful tools for describing quantum mechanical systems, including quantum communication and quantum information processing systems. It is shown that quantum communication channels with Gaussian noise and quantum teleportation of continuous variables are described by operational phase-space probability distributions. The relation of operational phase-space probability distribution to the extended phase-space formalism proposed by Chountasis and Vourdas is discussed.     

Quantum dynamics in ultracold atomic physics

We review recent developments in the theory of quantum dynamics in ultracold atomic physics, including exact techniques and methods based on phase-space mappings that are applicable when the complexity becomes exponentially large. Phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum Einstein-Podolsky-Rosen (EPR) entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorption, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.     

Fluctuations in hadronic and nuclear collisions

We investigate several fluctuation effects in high-energy hadronic and nuclear collisions through the analysis of different observables. To introduce fluctuations in the initial stage of collisions, we use the interacting gluon model (IGM) modified by the inclusion of the impact parameter. The inelasticity and leading-particle distributions follow directly from this model. The fluctuation effects on rapidity distributions are then studied using Landau's hydrodynamic model in one dimension. To investigage further the effects of the multiplicity fluctuation, we use the longitudinal phase-space model, with the multiplicity distribution calculated within the hydrodynamic model, and the initial conditions given by the IGM. Forward-backward correlation is obtained in this way.     

Statistical Mechanical Theory of a Closed Oscillating Universe

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy production of this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space.     

Comment on “Why the `coarse-graining' of Wigner function is always coarse” [Opt. Commun. 178 (2000) 147]

Incorrect statements and assumptions undermining the validity of the results presented in the above paper are pointed out and shortly discussed. It is stressed that a proper `coarse graining' of a Wigner phase-space distribution function cannot be in general performed over finite phase-space cells and that any `smearing' over infinite phase-space areas cannot violate the respective uncertainty relations, which furnishes an answer to the question asked in the title.     

Theory of Super Phase-Space Representations and Supercoherent States

The theory of a class of phase-space representations is developed for boson–fermion systems. The super phase-space operator is constructed and its properties are discussed. It is shown that the supersymmetric antinormal ordering rule corresponds to the supercoherent-state representation. Thus, the supersymmetric nature of the supercoherent states is revealed from the viewpoint of the phase-space representations.     

合肥光源相空间测量

 介绍了在合肥光源（HLS）上的相空间测量系统和测量结果,同时进行了工作点(Tune值)的计算。研究了电子储存环上三种相空间测量和计算方法：双位置单圈法、单位置双圈法和单位置单圈法。通过对仿真数据的计算和比较,论证了这三种方法的正确性和可行性,并分析了这三种方法的适用条件和在不同条件下的优缺点,为合肥光源的相空间测量提供了新的设计思路。     

Phase-space representation of quantum systems in the relative-state formulation

A phase-space representation of quantum systems within the framework of the relative-state formulation is proposed. To this end, relative-position and relative-momentum states are introduced and their properties are investigated in detail. Phase-space functions that represent a quantum state vector are constructed in terms of the relative-positive and relative-momentum states, and the quantum dynamics is investigated by using the phase-space functions. Furthermore, probability distributions in phase space are considered by means of the relativestate formulation, and it is shown that the phase-space probability distribution is closely related to the operational probability distribution. The marginal distribution, characteristic function, and operational uncertainty relation are also discussed.     

合肥光源相空间测量

介绍了在合肥光源（HLS）上的相空间测量系统和测量结果,同时进行了工作点(Tune值)的计算。研究了电子储存环上三种相空间测量和计算方法：双位置单圈法、单位置双圈法和单位置单圈法。通过对仿真数据的计算和比较,论证了这三种方法的正确性和可行性,并分析了这三种方法的适用条件和在不同条件下的优缺点,为合肥光源的相空间测量提供了新的设计思路。     

Lyapunov Instability for a Hard-Disk Fluid in Equilibrium and Nonequilibrium Thermostated by Deterministic Scattering

We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and under shear. The Lyapunov exponents are calculated using a recently developed formalism for systems with elastic hard collisions. The system is thermalized by deterministic and time-reversible scattering at the boundary, whereas the bulk dynamics remains Hamiltonian. This thermostating mechanism allows for energy fluctuations around a mean value which is reflected by only two vanishing Lyapunov exponents in equilibrium and nonequilibrium. In nonequilibrium steady states the phase-space volume is contracted on average, leading to a negative sum of the Lyapunov exponents. Since the system is driven inhomogeneously we do not expect the conjugate pairing rule to hold, which is indeed shown to be the case. Finally, the Kaplan–Yorke dimension and the Kolmogorov–Sinai entropy are calculated from the Lyapunov spectra.     

Quantum many-body simulations using Gaussian phase-space representations

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This paper traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices. The text was submitted by the authors in English.