Elements of reality,Lorentz invariance,and the product rule

Recently various gedankenexperiments have been formulated which argue that the assumption that elements of reality are Lorentz invariant cannot be reconciled with standard quantum mechanics. Two of these gedankenexperiments were subsequently analyzed using the notion of pre- and postselected quantum systems, and it was claimed that elements of reality can be made Lorentz invariant if the product rule of standard quantum mechanics is abandoned. In this paper we show that the apparent violations of the product rule in these gedankenexperiments are not as significant as they appeared to be in the previous analysis. We conclude that the problems with Lorentz invariance which arise in these gedankenexperiments are essentially unrelated to the product rule violations.     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.     

Ensemble interpretation of the EPR-Bell correlations

The EPR-Bell correlations between the spins of a pair of particles originally in a singlet state are discussed both on the basis of the mathematical formalism of quantum mechanics and the ensemble interpretation. It is shown that the correlations predicted by the mathematical formalism are in agreement with those expected on the basis of the ensemble interpretation, if the electrons are treated as distinguishable particles after they separate and undergo observation. In this case, the correlations are only in partial agreement with agedanken experiment of Mermin on the subject. It is pointed out, however, that agreement with Mermin’s conclusions is possible if one treats the electrons as indistinguishable even when they are subjected to observation after separation, though there is no obvious theoretical justification for doing so.     

Black hole remnants due to GUP or quantum gravity?

Based on the micro-black hole gedanken experiment as well as on general considerations of quantum mechanics and gravity the generalized uncertainty principle (GUP) is analyzed by using the running Newton constant. The result is used to decide between the GUP and quantum gravitational effects as a possible mechanism leading to the black hole remnants of about Planck mass.     

Can information be transferred faster than light? I. Agedanken device for generating electromagnetic wave packets with superoptic group velocity

Agedanken electromagnetic device is described which permits the transfer of information at speeds faster than light without violating the principle of causality.     

A critique of the disturbance theory of indeterminacy in quantum mechanics

Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this disturbance with the projection postulate. We present a critique of the disturbance theory based on the fact that the required disturbance will in general depend on the interaction time of the system and state-preparer. This point is exploited in the construction of a spin-interaction model which acts as a counterexample to the disturbance doctrine, while remaining faithful to the spirit of Heisenberg'sgedanken experiments. Several consequences of this result are discussed.This work formed part of a thesis submitted by one of us (HRB) in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the University of London.     

Tomita representation of the Arnol'd cat map

The Tomita Hilbert-space representation of the Arnol'd cat map model of Benattiet al. is described and the operators representing physical quantities are defined for the classical and quantum cases. It is seen that the exponential decay of correlations is preserved upon quantization.     

Optical control of the coherent dynamics of excitons in a semiconductor quantum well

The dynamics of the coherent superposition of exciton states in a semiconductor quantum well excited by the joint action of two successive light pulses with the time interval between them t ₁₂ has been theoretically studied. The dependences of the amplitude and initial phase of the quantum bits on t ₁₂ have been found. It has been shown that the time dependence of the Kerr rotation of the reflected probe pulse is determined not only by the dynamics of the excited state, but also by the optical properties of the heterostructure containing the quantum well. The dependence of the decay rate of the excited state on t ₁₂ has been predicted.     

Efficient scheme for entangled states and quantum information transfer with trapped atoms in a resonator

A protocol is proposed to generate atomic entangled states and implement quantum information transfer in a cavity quantum electrodynamics system. It utilizes Raman transitions or stimulated Raman adiabatic passages between two systems to entangle the ground states of two three-state Λ-type atoms trapped in a single mode cavity. It does not need the measurements on cavity field nor atomic detection and can be implemented in a deterministic fashion. Since the present protocol is insensitive to both cavity decay and atomic spontaneous emission, it may have some interesting applications in quantum information processing.     

The effect of atomic spontaneous decay on the dynamics of the negativity of the Wigner function of radiation

The exact solution of the master equation for the case of a high-Q cavity with atomic decay is found. We use the negativity of the Wigner function (WF) as an indicator of nonclassicality. It is found that the negative values of the field WF are very sensitive to any change in the damping parameter. The atomic spontaneous decay leads to the simultaneous disappearance of both entanglement and nonclassicality of quantum states. Moreover, the purity of the field states is completely lost.     

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

We study the deviations from the exponential decay law, both in quantum field theory (QFT) and quantum mechanics (QM), for an unstable particle which can decay in (at least) two decay channels. After a review of general properties of non-exponential decay in QFT and QM, we evaluate in both cases the decay probability that the unstable particle decays in a given channel in the time interval between t and t+dt. An important quantity is the ratio of the probability of decay into the first and the second channel: this ratio is constant in the Breit-Wigner limit (in which the decay law is exponential) and equals the quantity Γ ₁/Γ ₂, where Γ ₁ and Γ ₂ are the respective tree-level decay widths. However, in the full treatment (both for QFT and QM) it is an oscillating function around the mean value Γ ₁/Γ ₂ and the deviations from this mean value can be sizable. Technically, we study the decay properties in QFT in the context of a superrenormalizable Lagrangian with scalar particles and in QM in the context of Lee Hamiltonians, which deliver formally analogous expressions to the QFT case.     

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r ⁶ at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh ⁴ on, also decay as 1/r ⁶. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r ⁶, while the charge correlation decays faster, as 1/r ¹⁰. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.     

p-adic quantum mechanics

An extension of the formalism of quantum mechanics to the case where the canonical variables are valued in a field ofp-adic numbers is considered. In particular the free particle and the harmonic oscillator are considered. In classicalp-adic mechanics we consider time as ap-adic variable and coordinates and momentum orp-adic or real. For the case ofp-adic coordinates and momentum quantum mechanics with complex amplitudes is constructed. It is shown that the Weyl representation is an adequate formulation in this case. For harmonic oscillator the evolution operator is constructed in an explicit form. For primesp of the form 4l+1 generalized vacuum states are constructed. The spectra of the evolution operator have been investigated. Thep-adic quantum mechanics is also formulated by means of probability measures over the space of generalized functions. This theory obeys an unusual property: the propagator of a massive particle has power decay at infinity, but no exponential one.     

Coherent control of interference processes in radiative decays

Possibility of coherent control of spontaneous emission from four- and five-level system in the laser radiation field is studied. The four-level system consists of two levels resonantly driven by laser radiation where either of levels may decay to a separate level. For such a system, we show that the presence of the second decay channel may deteriorate the destructive interference occurring in case of one decay channel because of Autler-Townes effect. The five-level diagram represents two two-level resonantly driven systems with the upper levels decaying to a common level. For this diagram, interference between the two decay channels takes place and it is partially or completely destructive or constructive depending on the initial conditions and on the mutual orientation of the transition dipole moments. It is shown that population transfer takes place by the same quantum vacuum via spontaneous emission. The populations are shown to have damping oscillatory nature.     

Quantum measurement and pure dephasing

The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix _ρmα;nβ describing an interacting measured object and measuring device into a diagonal density matrix _{ρmα;mαδmnδαβ} . The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT ₂, the phase relaxation time, and much smaller thanT ₁, the population relaxation time:T ₂ ≪ Δt ≪T ₁. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials _z = −1/2 state into superposition ofs _z = ±1/2 states. The irreversible relaxation leads to the proper mixture ofs _z = 1/2 ands _z = −1/2 state. Results of the measurements are verified by the second electromagnetic pulse.     

非线性耗散对亚稳态系统量子衰变速率的影响

发展了一种快速傅里叶变换路径积分方法，研究非线性耗散系统的量子衰变速率，得到了Bounce轨道的作用量S_B，即衰变速率的指数因子.在系统与环境存在非线性耦合f(x)=tanh［λ(x-x_b)］的情形下，发现其对衰变速率具有抑制作用.指数因子随温度T的关系不再满足S_B=a［1-b(T/T_c)²］法则；与通常的线性耗散情形相比，跨越温度T_c回升，即系统更早地进入穿透区域. 关键词： 量子衰变 非线性耦合 路径积分 快速傅里叶变换     

类氢U91+离子的辐射复合及其辐射退激发过程的理论研究

基于多组态Dirac-Fock理论方法,利用GRASP92和RATIP以及在此基础上最新发展的RERR06程序,对类氢U⁹¹⁺（1s）离子的辐射复合截面以及辐射退激发过程进行了详细的理论研究.系统地计算了具有确定能量的连续电子被处于基态的类氢U⁹¹⁺（1s）离子俘获到nl （1≤n≤8, 0≤l≤6）轨道形成类氦U⁹⁰⁺（1snl）离子的辐射复合截面,并研究了这辐射复合末态退激发谱的相对强度.研究发现,类氢U⁹¹⁺（1s）离子辐射复合到不同轨道的截面随其主量子数的增大而显著减小;同时,辐射复合末态的退激发对Kα谱线的相对强度有重要影响. 关键词： 辐射复合 多组态Dirac-Fock理论方法 辐射退激发     

Aberration and the question of equivalence of some ether theories to special relativity

In the last two decades, theories explaining the same experiments as well as special relativity does, were developed by using different synchronization procedures. All of them are ether-like theories. Most authors believe these theories to be equivalent to special relativity, but no general proof was ever given. By means of agedanken experiment on light aberration, we produce strong evidence that this is the case for experiments made in inertial systems.