The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.Comment: 9 pages,Revte

Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.Comment: 12 pages,no figures,some corrections,new reference

Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature. The authors are of the opinion that the approach proposed may lead to proof of these relations. To this end, the statistical mechanics deformation at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Plank scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Plank's. The associated deformation of a canonical Gibbs distribution is given explicitly.Comment: 15 pages,no figure

Labor Law - Federal Pre-Emption - Limitations on State Jurisdiction in Causes Arising Out of Labor Disputes

Respondent employers refused to enter a union shop agreement with the petitioning unions, who then began to picket peacefully and to exert pressure on respondents\u27 suppliers and customers to persuade them to cease dealing with respondents. Respondents initiated a representation proceeding before the NLRB, which declined jurisdiction on the ground respondents\u27 business did not have a sufficient effect on commerce to meet the NLRB\u27s self-imposed jurisdictional standards. Respondents then sought and obtained damages and an injunction in the California courts. On certiorari to the United States Supreme Court the injunction order was reversed, but the question of damages was remanded to the state court since it was unclear whether the damages were sustained under California or federal law. The state court sustained the damages on the basis of state law. On certiorari to the United States Supreme Court, held, reversed, four justices concurring in result only. Absent an NLRB determination that an activity is neither protected nor prohibited, or compelling precedent applied to essentially undisputed facts, state courts have no jurisdiction to award damages for losses arising out of such activity even if based on tort liability theories under state law. San Diego Building Trades Council v. Garmon, 359 U.S. 236 (1959)

Constitutional Law - Due Process and Right of Confrontation- Jencks Act

The Jencks Act like the rule it purportedly reaffirmed, was designed to insure justice. Although the stated purpose of the act was to preserve the rights of any defendant under due process of law, the question remains unresolved whether, in articulating the rule in terms of justice, the Court in Jencks v. United States incorporated it into the requirements of due process. To be sure, the underlying intent of both the Court and Congress is unclear, but of far more concern than the intent is whether the Jencks Act, in fact, violates the constitutional mandates of the Fifth and Sixth Amendments, even if the Jencks case itself was not based on constitutional grounds. The Court in Jencks clarified four procedural matters dealing with a defendant\u27s right to inspect extra-judicial statements made by government witnesses to government agents: (1) defendant is not required to establish a foundation of inconsistency in order to inspect prior statements of witnesses; (2) whereas inspection of prior statements had formerly rested in the trial court\u27s discretion, the Jencks decision indicates that defendant is entitled to inspect them as a matter of right; (3) the Court specifically disapproved of the procedure whereby the requested documents are submitted to the trial judge for his determination of relevancy and materiality; (4) the Court ruled that a refusal by the government to comply with an order for production must result in a dismissal. As to (1) and (2), the act embodies the Court\u27s holding. With respect to (3) and (4), the act appears to limit the holding; this will be discussed later in this comment

Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure