Squeezed “atomic” states,pseudo-Hermitian operators and Wigner D-matrices

The states of N two-level atoms can be mapped onto the eigenvectors of angular momentum (with j=N/2) and this system in interaction with a radiation field constitutes a fundamental model in Quantum Optics. There from one may construct atomic coherent states and minimum uncertainty packets. The squeezing of such states is of considerable contemporary interest. We show that the properties of squeezed atomic states are most elegantly and economically expressed in terms of pseudo-Hermitian operators and through Wigner D-matrices and their analytical continuation.     

Coherent quantum oscillation trajectories

We discuss coherent oscillations in the quantum potential view of quantum mechanics, giving examples for both a superposition of position states, and a superposition of momentum states.     

Anti-photon

It should be apparent from the title of this article that the author does not like the use of the word photon, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the aether or vacuum to stand for empty space, even if no such thing existed. There are very good substitute words for photon, (e.g., radiation or light), and for photonics (e.g., optics or quantum optics). Similar objections are possible to use of the word phonon, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.It is a pleasure to join in the 60th birthday celebration of the Director, Herbert Walther, of the Max-Planck-Institute for Quantum Optics at Garching, and wish him much happiness and many more years of his very great scientific creativity.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Stationary non-equilibrium states of infinite harmonic systems

We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states, Gaussian measures on the phase space of the infinite system (analogues results are true for quantum systems). Their ergodic properties are the same as those of the equilibrium states: e.g. for ordered periodic crystals they are Bernoulli. Unlike the equilibrium states however they are not stable towards perturbations in the potential.We are particularly concerned here with states in which there is a non-vanishing steady heat flux passing through every point of the infinite system. Such superheat-conducting states are of course only possible in systems in which Fourier's law does not hold: the perfect harmonic crystal being an example of such a system. For a one dimensional system, we find such states (explicitely) as limits, whent, of time evolved initial states _i in which the left and right parts of the infinite crystal are in equilibrium at different temperatures, _L ^–L _R ^–1 , and the middle part is in an arbitrary state. We also investigate the limit of these stationary (t) states as the coupling strength between the system and the reservoirs goes to zero. In this limit we obtain a product state, where the reservoirs are in equilibrium at temperatures _L ^–1 and _R ^–1 and the system is in the unique stationary state of the reduced dynamics in the weak coupling limit.On leave of absence from the Fachbereich Physik der Universität München. Work supported by a Max Kade Foundation FellowshipResearch supported in part by NSF Grant MPS75-20638     

Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.     

Role of time in the sum-over-histories framework for gravity

I sketch a self-contained framework for quantum mechanics based on its path-integral or sum-over-histories formulation. The framework is very close to that for classical stochastic processes like Brownian motion, and its interpretation requires neither measurement nor state-vector as a basic notion. The rules for forming probabilities are nonclassical in two ways: they use complex amplitudes, and they (apparently unavoidably) require one to truncate the histories at a collapse time, which can be chosen arbitrarily far into the future. Adapting this framework to gravity yields a formulation of quantum gravity with a fully spacetime character, thereby overcoming the frozen nature of the canonical formalism. Within the proposed adaptation, the value of the collapse time is identified with total elapsed spacetime four-volume. Interestingly, this turns the cosmological constant into an essentially classical constant of integration, removing the need for microscopic fine tuning to obtain an experimentally viable value for it. Some implications of the V = T rule for quantum cosmology are also discussed.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

On the electromagnetic structure of elementary particles

Using modern similarity and dimensionality methods, criteria of similarity are derived and used as transformations, which effect the conversion from one natural system of units to another. The exclusion principles thus defined are used to determine the powers of the similarity criteria in quantitative relations.Systems of units of the fermion and boson types are used in the simplest identification of the parameters corresponding to elementary particles.A set of electric and magnetic physical constants with dimensionality length, area, and volume, is obtained and successfully unified within the limits of a vortex ring, the maximum dimensions of which are defined by the Compton wavelength, and the minimum by the classical radius of the particle. The vortex ring model is in accordance with the latest experimental data, and it enables the behavior of the incident and target particles in the scattering process to be predicted.In modern theoretical physics the elementary particles are still considered as essentially structureless point formations, and hence it is impossible to give a purely theoretical treatment of the structure of the particles. Thus the various attempts in this direction (Hofstadter, Blokhintsev) have a polyphenomenological character and are internally inconsistent. (The search for the structure of an elementary particle is carried out on the assumption that it is not elementary, since truly elementary particles are defined as point size.) The author recognizes the need for an original approach to the structure of elementary particles, based on a method of study adequate for the problem. Such a method is the theory of dimensionality and similarity (Sedov, Gukhman, and Kirpichev), which serves as a scientific basis of a physical experiment (Kirpichev), or as the scientific basis for a model of the phenomena, insofar as the criteria of similarity are a reflection of the physical model of the process (Gukhman).It is a pleasure to thank Academician L. I. Sedov and Professor K. A. Putilov for valuable criticism and advice, and Professor A. S. Irisov and V. V. Lokhin for useful discussions.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

The first and second nearest neighbour Cr3+ pairs in ruby

The irreducible representations of the states of the first and second nearest neighbour Cr³⁺ pairs in ruby were deduced from the known states of the single ions by the group theoretical method of induction. The summetry selection rules and polarizations for electric dipole radiation are discussed.Supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 65 Frankfurt-Darmstadt.     

Bell-type inequalities in the nonideal case: Proof of a conjecture of bell

Recently Bell has conjectured that, with epsilonics, one should be able to argue, à la EPR, from almost ideal correlations (in parallel Bohm-Bell pair experiments) to almost determinism, and that this should suffice to derive an approximate Bell-type inequality. Here we prove that this is indeed the case. Such an inequality—in principle testable—is derived employing only weak locality conditions, imperfect correlation, and a propensity interpretation of certain conditional probabilities. Outcome-independence (Jarrett's completeness condition), hence factorability of joint probabilities, is not assumed, but rather an approximate form of this is derived. An alternative proof to the original one of Bell [1971] constraining stochastic, contextual hidden-variables theories is thus provided.     

Topologies for Lorentz manifolds: The space topology

The main result in this note states and proves that the space topology for Lorentz manifolds is 0-semimetrizable. This is in a certain sense the spacelike version of an analogous result for the Hawking-King-McCarthy path topology, which was published in [5]. But the proofs are completely different. The space topology is the finest topology on a Lorentz manifold, which induces the manifold topology on every spacelike hypersurface. Its geometric significance comes from the fact, that its full homeomorphismgroup is the group of all conformal diffeomorphisms. 0-semimetrics are very natural generalizations of metrics and have interesting interpretations as statistical metrics and as metrics with an elementary length.This paper is dedicated to Hans Vogler on the occasion of his fiftieth birthday.     

Diffusion of interacting particles on a percolating lattice

The diffusion has been simulated by the Monte Carlo method on a random lattice. As in the ant in the labyrinth problem the particles move by stepping to allowed, randomly chosen neighboring fields. The particle interaction has been defined by the constraint that only one particle can occupy a site at a time. Biased diffusion means that one of the directions will be chosen with a greater probability than the others. It was shown that, with an increasing number of walkers, the displacement of the particles first of all increases to a maximum value and then decreases. This filling-up effect will not occur with small bias fields and on lattices with a high concentration of allowed sites.     

Simulated Annealing for “spin-glass-like” optimization problems

A general recipe for the use of Simulated Annealing for spin-glass-likeNP-complete problems is provided. The classification principles of spin-glass-like problems are discussed. This class of problems is conjectured to incorporate a large variety of complex problems from economics and biology to every day life. We particularly stress the importance for optimization problems in physics. The application to the placement of chip-design is discussed from the point of view of spin-glass research.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

Traffic Jams in a Lattice-Gas Model

We propose a simple lattice-gas model characterized by two states of atoms, the thermalized state, which is the same as in the standard lattice-gas model, and the running state, where the atoms jump in one direction only. The model exhibits the existence of traffice jams (bunching of thermalized atoms in compact groups), the nonlinear dependence of mobility on the jump probability, and the hysteresis.     

A phase cell approach to Yang-Mills theory

Variables are chosen to describe the continuum Yang-Mills fields, a discrete set of group valued variables. These are group elements associated to the sequence of lattice field theory configurations realizing the continuum field. The field is laid down inductively. At each inductive step one of three types of field excitations makes its contribution to the total field. These are either pure modes, averaging correction modes, or chunks. The pure modes are small field excitations, as studied in previous papers in this series [2,3]. The averaging correction modes are small excitations added to make sure the block spin transformation is satisfied at each edge. The chunks, encompassing most of our difficulties, are large field excitations. Topological obstructions in ₃(G) must be dealt with in defining a gauge choice for each chunk. The laying down process is complex, but fiendishly clever, ensuring a principle of gauge invariant coupling. Each group valued variable is either the amplitude of a pure mode or an internal variable in a chunk. The amplitude of an averaging correction mode is a dependent variable, a function of the (independent) variables used to describe the field. The (independent) variables herein defined are those whose mutual interaction will later be inductively decoupled in defining the phase cell cluster expansion (of course treating the variables of each chunk as a unit).This work was supported in part by the National Science Foundation under Grant No. PHY-85-02074     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.