On the adiabatic limit of Hadamard states

We consider the adiabatic limit of Hadamard states for free quantum Klein–Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein–Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron–Seiler–Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state.     

Geometric curvature and phase of the Rabi model

We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.     

Local quasiequivalence and adiabatic vacuum states

The problem of determining the physically relevant states acquires a new dimension in curved spacetime where there is, in general, no natural definition of a vacuum state. It is argued that there is a unique local quasiequivalence class of physically relevant states and it is shown how this class can be specified for the free Klein-Gordon field on a Robertson-Walker spacetime by using the concept of an adiabatic vacuum state. Any two adiabatic vacuum states of order two are locally quasiequivalent.     

Proliferation of atomic wave packets at the nodes of a standing light wave

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.     

Model basis states for photons and "empty waves"

From the perspective of physical realism (PR), a photon is a localized entity that carries energy and momentum, and which is surrounded by a wave packet (anempty wave) that is devoid of observable energy or momentum. In creating quantized PR basis states for a photon wave packet, three requirements must be met:(1) The basis states must each carry the frequency of the wave;(2) They must closely resemble the photon, so that e.g. they scatter in the same manner from an optical mirror;(3) They must have infinitesimal energy, linear momentum, and angular momentum. An essentially zero-energy "empty wave" quantum-a "zeron"-is defined which meets these requirements. It is created as an asymmetric single-particle (or single-antiparticle) excitation of the vacuum state, with the "particle" (or "antiparticle") and its associated "hole" (or "antihole") forming a rotational bound state. The photon is reproduced as a symmetric particle-antiparticle excitation of the vacuum state, with the "particle" and "antiparticle" also forming a rotational bound state. The relativistic transformation problem is discussed. A key point in this development is the deduction of the correct equation of motion for a "hole" state in an external electrostatic field.     

The normal-form (In)dependence of the adiabatic particle definitions

The adiabatic particle definition of Parker [1] has only been discussed for particular choices of the field variable and time coordinate, referred to here as the choice of a normal-form. It seems to have been implicitly assumed that the associated vacuum is independent of the normal-form chosen; we show that this is indeed the case.NATO Postdoctoral Fellow.     

单晶铜中冲击波阵面结构的数值模拟研究

 用分子动力学方法模拟计算了在初始温度为0 K时单晶铜中的冲击波结构,相互作用势采用铜的嵌入原子势（EAM）,模拟计算结果表明即使是在初始温度为0 K的FCC晶体中,冲击波波阵面后的区域也会向平衡态演化。局域分析表明冲击波阵面后区域的压力、粒子速度、应变和温度随时间逐步变化到稳定态,在所研究的冲击波强度（约262 GPa）下,波后区域的平均压力、粒子速度、应变均在约1 ps内逐渐上升并达到稳定值。动能温度在波阵面处始终为最大值,随着冲击波的传播,波后非零温度区域逐渐扩大,不同时刻的粒子速度分布函数说明波后区域逐渐向热力学平衡态演化,并最终达到热力学平衡,进一步的分析说明局域平衡是系统向平衡态演化的基本过程。     

State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields

Our formalism, described recently in (C. E. Dolby and S. F. Gull, Ann. Phys.293 (2001), 189-214.) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called adiabatic electric field. Several problems are resolved by incorporating the Bogoliubov coefficient approach and the tunnelling approach into a single consistent, gauge invariant formulation. The value of a time-dependent particle interpretation is demonstrated by presenting a coherent account of the time-development of the particle creation process, in which the particles are created with small momentum (in the frame of the electric field) and are then accelerated by the electric field to make up the bulge of created particles predicted by asymptotic calculations [2, 3]. An initial state comprising one particle is also considered, and its evolution is described as being the sum of two contributions: the sea of current produced by the evolved vacuum and the extra current arising from the initial particle state.     

Confinement of charged particles by an electromagnetic wave leaving the region of a strong gravitational field

The interaction of a charged particle in vacuum with a circularly polarized wave leaving the region of a strong static gravitational field in the direction of a magnetostatic field is considered. It turns out that this combination of fields forms, generally speaking, two capture regions (CR₁ and CR₂) on the phase cylinder of the particle. The evolution of these regions is determined by the gravitational field. The influence of the gravitational field on the rigidity of confinement of the particle in one of these regions (CR₁) is investigated. It is shown that the rigidity of confinement of particles with relatively high energies may increase toward the periphery of the gravitational field. The possibility of particle escape by the wave is demonstrated for particles whose initial energy is insufficient to leave the gravitational field region in the absence of the wave. In this case, the particle is trapped by the wave in CR₁ and subsequently confined. The mechanism of trapping the particle is discussed. Taganrog State Radio-Engineering University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–10, June, 2000.     

Superposition of Fock states via adiabatic passage in a coupled four-level atom－cavity system

We have investigated the behaviour of an atom－cavity system via a stimulated Raman adiabatic passage technique in a four-level system, in which two dark states are present. We find, because of the coherent control field, that a superposition of Fock states can be prepared, even when the cavity is initially not in its vacuum state. This method provides a way to generate arbitrary quantum states of a cavity field.     

Adiabatic Interpretation of Particle Creation in a de Sitter Universe

The choice of vacuum state for a quantum scalarfield (massive and arbitrarily coupled to thegravitational field, with coupling constant )propagating in a de Sitter spacetime is discussed. Theproblem of finite-time initial conditions for the modefunctions is analyzed, as well as how these determinethe vacuum state of the quantum system. The principleguiding the choice of vacuum state is the following: one wants the vacuum contribution to theenergy-momentum tensor to contain all the ultravioletdivergent terms, so that the particle creation terms arefinite, and covariantly conserved. There is a suitable set of modes (instantaneous adiabatic basis) inwhich this splitting of the expectation value of theenergymomentum tensor can be carried out. Numericalresults are presented for different initial times and the following values for the mass and thecoupling constant: m = 0.6, = 1/6. The nature ofthe particle creation effect is described and itsrelationship to the concept of a horizon crossing time is shown. These numerical results imply thatback reaction can be important and should be the subjectof further research.     

Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for the motion of shallow water, from the Navier-Stokes system for incompressible flows with a moving free surface [14]. These compressible systems are degenerate when vacuum state appears. We study initial-boundary-value problems for such systems for both bounded spatial domains or periodic domains. The dynamics of weak solutions and vacuum states are investigated rigorously. First, it is proved that the entropy weak solutions for general large initial data satisfying finite initial entropy exist globally in time. Next, for more regular initial data, there is a global entropy weak solution which is unique and regular with well-defined velocity field for short time, and the interface of initial vacuum propagates along the particle path during this time period. Then, it is shown that for any global entropy weak solution, any (possibly existing) vacuum state must vanish within finite time. The velocity (even if regular enough and well-defined) blows up in finite time as the vacuum states vanish. Furthermore, after the vanishing of vacuum states, the global entropy weak solution becomes a strong solution and tends to the non-vacuum equilibrium state exponentially in time.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

Asymptotic stability of stationary states in the wave equation coupled to a nonrelativistic particle

We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition, which is a version of the “Fermi Golden Rule.” We prove that in the large time approximation, any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.     

Ion charge state distributions of alloy-cathode vacuum arc plasmas

Ion charge state distributions (CSD's) of alloy-cathode vacuum arc plasmas have been calculated under the assumption that thermodynamic equilibrium is valid in the vicinity of the cathode spot, and equilibrium CSD's “freeze” when the plasma is rapidly expanding. In this way, experimental data of titanium-hafnium alloy-cathode plasmas have been simulated using a system of Saha equations generalized for multiple elements. It was found that the CSD's of titanium and hafnium freeze approximately at the same plasma temperature and density. The freezing parameters depend slightly on the plasma composition. For the example considered, freezing occurs at temperature of T=3.0-3.8 eV and a total heavy particle density of order 10²⁵m^-3     

Particle creation and warm inflation

During cosmological inflation, it has been suggested that fields coupled to the inflaton can be excited by the slow-rolling inflaton into a quasi-stable non-vacuum state. Within this scenario of “warm inflation”, this could allow for a smooth transition to a radiation dominated Universe without a separate reheating stage and a modification of the slow roll evolution, as the heat-bath backreacts on the inflaton through friction. In order to study this from first principles, we investigate the dynamics of a scalar field coupled to the inflaton and N   light scalar boson fields, using the 2PI-1/N$1/N$ expansion for nonequilibrium quantum fields. As a first step we restrict ourselves to Minkowski spacetime, interpret the inflaton as a time-dependent background, and use vacuum initial conditions. We find that the dominant effect is particle creation at late stages of the evolution due to the effective time-dependent mass. The further transfer of energy to the light degrees of freedom and subsequent equilibration only occurs after the end of inflation. As a consequence, the adiabatic constraint, which is assumed in most studies of warm inflation, is not satisfied when starting from an initial vacuum state.     

On the possibility of natural formation of a transverse wave with a phase velocity lower than the velocity of light

The formation of a transverse wave with a phase velocity lower than the velocity of light, which can exist in an equilibrium plasma without a slow-wave structure in zero magnetic field, is described. It involves the transformation of a transverse wave with trapped electrons, traveling along the magnetic field, into a slow transverse wave after the removal of the magnetic field. During the evolution of the wave with trapped electrons, the magnetic induction decreases very slowly in the direction of the wave propagation. As a result, the velocity at which electrons are in resonant interaction with the wave increases; therefore, the electrons fall to the bottom of potential wells. Under the influence of the trapped electrons, the phase velocity of the wave decreases and becomes lower than the velocity of light. It becomes equal to the velocity at which the electrons are in resonance interaction with the wave at the instant when the magnetic field vanishes. It is demonstrated that a transverse wave with a velocity lower than the velocity of light can exist in an equilibrium plasma even after the magnetic field vanishes; in this case, the flow of trapped electrons serves as a slow-wave structure.