Global Existence of Classical Solutions to the Fokker-Planck-BGK Equation

A kinetic model of the Fokker-Planck-Boltzmann equation is introduced by replacing the original Boltzmann collision operator with the Bhatnagar-Gross-Krook collision model (BGK collision model). This model equation, which we call the Fokker-Planck-BGK equation, has many physical features that the Fokker-Planck-Boltzmann equation possesses. We first establish an L ^∞ existence result for this equation, by which we construct the approximate solutions. Then, by means of the regularizing effects of the linear Fokker-Planck operator and L ^p estimates of local Maxwellians, we obtain some uniform estimates of the approximate solutions. Finally, combining those estimates and regularizing effects, we prove by a compactness argument that the equation has a global classical solution under rather general initial conditions. Supported by the Scientific Research Foundation of Huazhong University of Science and Technology (HUST-SRF).     

On the Discrimination Between Classical and Quantum States

With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.     

Distributional and Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials with Integrable Angular Cross Section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming S ^n?1 integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel–Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes the large data near local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in (Alonso et al. in Convolution inequalities for the Boltzmann collision operator. arXiv:0902.0507 [math.AP]) , by E. Carneiro and the authors, that allows us to show such propagation without additional conditions on the collision kernel. Finally, an L ^p -stability result (with 1≤p≤∞) is presented assuming the aforementioned condition.     

Quantization of Two Classical Models by Means of the BRST Quantization Method

An elementary gauge-non-invariant model and the bosonized form of the chiral Schwinger model are introduced as classical theories. The constraint structure is then investigated. It is shown that by introducing a new field, these models can be made gauge-invariant. The BRST form of quantization is reviewed and applied to each of these models in turn such that gauge-invariance is not broken. Some consequences of this form of quantization are discussed.     

Probability Description and Entropy of Classical and Quantum Systems

Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.     

Quantum Mechanics as a Simple Generalization of Classical Mechanics

A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices.     

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.     

Classical and Non-relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles

A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter.     

On Close Relationship Between Classical Time-Dependent Harmonic Oscillator and Non-relativistic Quantum Mechanics in One Dimension

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schrödinger’s equation. These results, with support from numerical simulations, strongly suggest that two uncoupled classical harmonic oscillators, which initially have a 90° relative phase shift and then are simultaneously disturbed by the same parametric perturbation of a finite duration, manifest behavior which can be mapped to that of a single quantum particle, with classical ‘range relations’ analogous to the uncertainty relations of quantum physics.     

Bohmian Mechanics,the Quantum-Classical Correspondence and the Classical Limit: The Case of the Square Billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.     

Classical interpretations of relativistic precessions

Relativists have exposed various precessions and developed ingenious experiments to verify those phenomena with extreme precisions. The Gravity Probe B mission was designed to study the precessions of the gyroscopes rotating round the Earth in a nearly circular near-Earth polar orbit to demonstrate the geodetic effect and the Lense-Thirring effect as predicted by the general relativity theory. In this paper, we show in a very simple and novel analysis that the precession of the perihelion of Mercury, the Thomas precession, and the precession data （on the de Sitter and Lense-Thirring precessions） collected from the Gravity Probe B mission could easily be explained from classical physics, too.     

Quantum Computing’s Classical Problem,Classical Computing’s Quantum Problem

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classical computers can already do. At the same time, those classical computers continue to advance, but those advances are now constrained by thermodynamics, and will soon be limited by the discrete nature of atomic matter and ultimately quantum effects. Technological advances benefit both quantum and classical machinery, altering the competitive landscape. Can we build quantum computing systems that out-compute classical systems capable of some \(10^{30}\) logic gates per month? This article will discuss the interplay in these competing and cooperating technological trends.     

Classical dynamics of laser-driven D₃⁺

A classical model of the triatomic D?? molecule subjected to an intense, few-cycle laser pulse is introduced. The model is capable of describing the laser-induced correlated motion of both electrons and nuclei in three dimensions, and allows us to follow the motion of the two electrons and three deuterons from the initial field-free state, during the pulse, and until the bond breaking into the final fragments. By averaging over many trajectories, we calculate the relative yields of the ionization and dissociation channels, as well as the kinetic energy release (KER) from the fragment ions. A comparison with recent experimental KER spectra shows good qualitative agreement. In addition, we find a pathway in which an emitted electron recombines into a high-lying Rydberg state, resulting in D + D? + D? fragments with the same KER as in the D? + D? + D? channel.     

New physics contribution to neutral trilinear gauge boson couplings

We study the one-loop new physics effects to the CP even triple neutral gauge boson vertices γ ^⋆ γ Z, γ ^⋆ Z Z, Z ^⋆ Z γ and Z ^⋆ ZZ in the context of Little Higgs models. We compute the contribution of the additional fermions in Little Higgs models in the framework of direct product groups where [SU(2)×U(1)]² gauge symmetry is embedded in SU(5) global symmetry and also in the framework of the simple group where SU(N)×U(1) gauge symmetry breaks down to SU(2) _L ×U(1). We calculate the contribution of the fermions to these couplings when T parity is invoked. In addition, we re-examine the MSSM contribution at the chosen point of SPS1a′ and compare with the SM and Little Higgs models.     

Spectroscopy of laser-produced cerium plasma for remote isotope analysis of nuclear fuel

A cerium oxide sample was ablated by 2nd harmonic radiation of Nd:YAG laser at a power density of 0.1 GW/cm². Time evolution of the ablation plume was investigated by laser absorption time-of-flight (TOF) measurement. It was found that the ablated ionic plume in vacuum consisted of two components having different velocities whereas the ablated neutral atoms had mainly a single component. The flow velocity perpendicular to the sample surface in vacuum was determined to be 3.5 km/s for neutral atoms, and 4.7 km/s and 9.3 km/s for singly charged ions. From the detailed plume evolution in ambient atmosphere with several pressures we obtained some experimental conditions suitable for isotope analysis of atomic cerium.     

Interpreting near-side correlations and the RHIC beam energy scan

Recent data from heavy ion collisions at RHIC show strong near-side correlations extending over several units of rapidity. This ridge-like correlation exhibits an abrupt onset with collision centrality. In this talk, I argue that the centrality and beam-energy dependence of these near-angle correlations could provide access to information about the Quark Gluon Plasma phase boundary and the Equation of State of nuclear matter. A beam-energy-scan at RHIC will better reveal the true source of these correlations and should be a high priority at RHIC.     

Cross-sections of large-angle hadron production in proton– and pion–nucleus interactions II: beryllium nuclei and beam momenta from ±3 GeV/c to ±15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons and charged pions, in the interactions with a 5% λ _abs thick stationary beryllium target, of proton and pion beams with momentum from ±3 GeV/c to ±15 GeV/c. Results are given for secondary particles with production angles 20° <θ<125°.     

Classical space–times from the S-matrix

We show that classical space–times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space–time as a series in _GN$G_N$. At no point of the derivation is any use made of the Einstein–Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space–time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space–times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang–Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.