Causal stochastic interpretation of quantum statistics

The differences between Einstein and Bohr on the interpretation of quantum mechanics revolved around the question of completeness of the Copenhagen Interpretation. This fundamental problem is examined here in the light of recent neutron interference experiments which allow for novel experimental situations. Exploiting the possibility of neutron spin flip in these experiments, the inadequacy of the Copenhagen interpretation to fully understand the experimental results is brought out. Instead a causal interpretation of quantum mechanics is advocated, in which the neutron, as a particle, does always have a definite space time trajectory but also involves a wave which creates a potential affecting the particle neutron. The reestablishment of definite particle trajectories in the microscopic domain obliges us to reexamine the statistical treatment of ‘identical’ particles, as well as the problem of negative energies and probabilities in relativistic quantum mechanics.     

基于Tavis-Cummings模型实现非定域三原子系统量子特性的远程控制

运用全量子理论并结合数值计算方法,研究了三个二能级原子系统的量子特性。初始三原子处于W纠缠态,让其中的两原子A、B与相干态光腔场发生共振作用,经腔QED演化以后,对原子进行Bell基测量,通过调节相干态光场的强度和原子间的偶极相互作用,来控制腔外原子C的布居差演化;对相干态光场进行光子探测,通过改变探测到的光子数、相干光场参量和原子间偶极相互作用,来控制腔外原子C的偶极压缩,最终实现了远程操纵腔外原子非经典特性的目的。     

Causal independence of free quantum fields

Causal independence of local observable algebras for free Dirac field, free electromagnetic field and free scalar massless field is proved. A method suggested for the proof is based on the noncommutative probability theory technique.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles. Liblice castle, Czechoslovakia, June 18–23, 1978.     

Renormalizations in quantum statistics

A simple proof is given that quantum statistics is multiplicatively renormalizable (if the corresponding quantum field theory is), that the renormalization constants are independent of the temperature and the parameters in the theory with the dimensions of mass, and that the renormalization constants (of the counterterms) are equal to the renormalization constants of the corresponding quantum field theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 26–30, January, 1981.I should like to thank B. L. Voronov, O. K. Kalashnikov, A. D. Linde, E. S. Fradkin, and A. E. Shabad for helpful discussions.     

Implementation of non-local quantum controlled-NOT gate with multiple targets

We show how a non-local quantum controlled-NOT (CNOT) gate with multiple targets can be implemented with unit fidelity and unit probability. The explicit quantum circuit for implementing the operation is presented. Two schemes for probabilistic implementing the operation via partially entangled quantum channels with unit fidelity are put forward. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different.     

New forms of quantum statistics

We propose a new two-parameter deformation of the algebra of creation and destruction operators, which allows the construction of a new family of Hillbert spaces with positive definite inner product. This provides a continuous interpolation between two new forms of statistics named orthofermi and orthobose statistics. Positivity of the inner product over the two-parameter region is discussed.     

Boltzmann statistics of quantum friction

In this paper we investigate the thermodynamic properties of simple quantum-mechanical systems in the presence of friction. Using the propagators for these simple models we calculate the response functions in Boltzmann statics. In the low temperature region the response functions exhibit singular behaviour.     

Lie algebraic aspects of quantum statistics. parafermi statistics

We study in detail the Lie-algebraical properties of the quantization condition for spinor fields

$\text{[a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{,a}{}^{\mathrm{?}}{}_{\mathrm{j}}\text{],a}{}^{\mathrm{\pm }}{}_{\mathrm{i}}\text{= ±2δ}{}_{\mathrm{ij}}\text{a}{}^{\mathrm{\pm }}{}_{\mathrm{j}}$

.It turns out that the parafermi statistics is one particular solution of this relation: it is the minimal rank simple Lie algebra generated by the operators a^±_i entering into the above relation. We point out some other solutions.     

Causal interpretation and quantum phase space

We show that the de Broglie–Bohm interpretation can be easily implemented in quantum phase space through the method of quasi-distributions. This method establishes a connection with the formalism of the Wigner function. As a by-product, we obtain the rules for evaluating the expectation values and probabilities associated with a general observable in the de Broglie–Bohm formulation. Finally, we discuss some aspects of the dynamics.     

Towards UV finite quantum field theoriesfrom non-local field operators

A non-local toy model whose interaction consists of smeared, non-local field operators is presented. We work out the Feynman rules and propose a power counting formula for arbitrary graphs. Explicit calculations for one loop graphs show that their contribution is finite for sufficient smearing and agree with the power counting formula. UV/IR mixing does not occur.Received: 26 February 2004, Published online: 5 May 2004     

Produced entropy in quantum statistics

Hg-films were condensed with admixtures of HgBr₂ or HgCl₂ onto a substrate at 4.2 °K. The superconducting transition temperature is measured as a function of the impurity concentration. The transition temperature increases from 3.96 °K of the pure quenched film to 4.06 °K at a content of 0.3 mol.% HgBr₂. Higher impurity concentrations lower the transition temperature and superconductivity vanishes at about 16 mol.% HgBr₂ or 23 mol.% HgCl₂ respectively. Above these concentrations the electrical resistivity shows a negative temperature coefficient. By means of Debye-Scherrer diagrams there is found a diminishing of the crystallite size with increasing impurity concentration.     

Entanglement concentration using quantum statistics

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Because of the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.     

Eigenfunction statistics on quantum graphs

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.     

Search for elementary quantum statistics

Bose-Einstein and Fermi-Dirac are the main quantum statistics. Therefore, it is likely that if truly elementary building blocks of Nature exist, they are either bosons or fermions, so that it is also likely that one, and only one, of the following possibilities, concerning those elementary building blocks, is correct: (i) all of them are fermions; (ii) some of them are bosons, others fermions; (iii) all of them are bosons; (iv) the distinction between these cases is methodological, not physical. Since tensors can be constructed from spinors, most physicists support one of the first two points of view. However, by starting from the fact that now it is known that bosonization makes sense, and developing a former research by Penney, we defend the point of view that, at least in a finite model of the Universe, the third point of view is the more likely. To avoid confusion we state that we are not concerned with the whole set of the so-called “elementary particles” since most physicists believe by now that, e.g., hadrons are built from quarks, nor concerned with quarks since many physicists suspect they are also composite objects. This research concerns the true elementary building blocks of Nature, assuming that such set exists, whatever those building blocks are. Finally, we extend this research to general finite associative algebras, enlarging the physical applicability of our point of view concerning the role of bosons in Nature.     

The hidden phase of Fock states; quantum non-local effects

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better defined, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, analogous to the pointer of a measurement apparatus, which illustrates the non-locality of standard quantum mechanics with particular clarity. The effect can be described as the teleportation at arbitrary distances of the continuous classical result of a local experiment. The EPR argument, transposed to this case, takes a particularly convincing form since it does not involve incompatible measurements and deals only with macroscopic variables.     

Spin and statistics of quantum kinks

Apart from some brief and inconclusive remarks concerning the problem of spin and statistics of quantum kinks in space-time dimension D > 2, we give a detailed discussion of the D = 2 situation. Our main results is that two-dimensional quantum kinks are statistical “schizons”; they exist in the same Hilbert space either as bosons or as fermions. In those cases where one can introduce local kink-sector generating operators as in the sine-Gordon model, the Bose and Fermi fields are strictly local fields, which are relatively non-local with respect to each other.