Quantum features in statistical observations of "timeless" classical systems

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the discrete physical time. This is motivated by studies of ``timeless'' reparametrization invariant models, where discrete physical time has recently been constructed based on coarse-graining local observables. Describing such deterministic classical systems with the help of path-integrals, primordial states can naturally be introduced which follow unitary quantum mechanical evolution in suitable limits.Comment: 7 pages. Invited talk at Int. Workshop Trends and Perspectives on Extensive and Non-Extensive Statistical Mechanics, Angra dos Reis (Brazil), Nov. 2003. To appear in Physica

Vacuum-Induced Quantum Decoherence and the Entropy Puzzle

Or: ``How to generate an ensemble in a single event?'' Following recent work on entropy in strong interactions, I explain the concept of environment-induced quantum decoherence in elementary quantum mechanics. The classically chaotic inverted oscillator becomes partially decoherent already in the environment of a single other oscillator performing only vacuum fluctuations. One finds exponential entropy growth in the subsystem with a Lyapunov exponent, which approaches the classical one for weak coupling. Presented at the Workshops on ``Quantum Infrared Physics'', Paris, 6 - 10.6.94, and ``QCD 94'', Montpellier, 7 - 13.7.94. Invited talk at the NATO Adv. Res. Workshop on ``Hot Hadronic Matter'', Divonne, 27.6. - 1.7.94. To appear in the Proceedings.Comment: 12 pages, CERN-TH.7372/9

Lithuanian Retail Internationalization: Features and Prospects

Purpose of the article: To distinguish and describe Lithuanian retail internationalization of the peculiarities in the last twenty-four years and bases on the changes in the future. Methodology/methods: The retail internationalization literature explores the theories, concepts, experiences in different countries is the methodological basis for the assessment of the process and the prospect of these process changes in Lithuania. Lithuanian retail internationalization progress of the investigation from the beginning, development and future prospects is divided into three phases. From a methodological point of view, this is a difficult research because even after twenty years. Scientific aim: To analyse retail internationalization process in Lithuania – features and prospects. Findings: Investigate and evaluate three Lithuanian retail internationalization stages showed that each of them has distinct features. A survey of retailers allowed to set retail internationalization level in 2013. Conclusions: The retail trade internationalisation process in Lithuania, which started immediately after the destruction of the socialist economy and proceeded as the foundation for market economy was being laid, was particular in the sense that famous foreign retail trade companies did not immediately enter the Lithuanian retail market. The characteristic feature of the process in Lithuania was the establishment of joint capital companies, while individual foreign businessmen often started their business in the country by opening their first store. Research limitations: no interest of retailers to be in contact regarding research and wide theme was as serious limitations to find out and explore the Lithuanian retail internationalization features. This is the original article, exploring the small market of retail internationalization process characteristics from its beginning until 2014

Four questions for quantum-classical hybrid theory

Four questions are discussed which may be addressed to any proposal of a quantum-classical hybrid theory which concerns the direct coupling of classical and quantum mechanical degrees of freedom. In particular, we consider the formulation of hybrid dynamics presented recently in Ref.[1]. This linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fulfil all consistency requirements discussed in the literature, while earlier attempts failed. - Here, we additionally ask: Does the theory allow for superposition, separable, and entangled states originating in the quantum mechanical sector? Does it allow for "Free Will", as introduced, in this context, by Diosi [2]. Is it local? Does it provide hints for the emergence of quantum mechanics from dynamics beneath?Comment: 16 pages - based on talk at the Conference on Emergent Quantum Mechanics / Heinz von Foerster Congress (Vienna University, Nov. 11-13, 2011

Quantum Mechanics and Discrete Time from "Timeless" Classical Dynamics

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless'' reparametrization invariant model of a relativistic particle with two compactified extradimensions. In this example, discrete physical time is constructed based on quasi-local observables. - Generally, employing the path-integral formulation of classical mechanics developed by Gozzi et al., we show that these deterministic classical systems can be naturally described as unitary quantum mechanical models. The emergent quantum Hamiltonian is derived from the underlying classical one. It is closely related to the Liouville operator. We demonstrate in several examples the necessity of regularization, in order to arrive at quantum models with bounded spectrum and stable groundstate.Comment: 24 pages, 1 figure. Lecture given at DICE 2002. To be published in: Decoherence and Entropy in Complex Systems, Lecture Notes in Physics (Springer-Verlag, Berlin 2003). - Comprises quant-ph/0306096 and gr-qc/0301109, additional reference

Determinism and a supersymmetric classical model of quantum fields

A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a positivity constraint on physical states, which is invariant under the classical Hamiltonian flow. In this way, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. Thus, 't Hooft's proposal to reconstruct quantum theory as emergent from an underlying deterministic system, is realized here for a field theory. Quantization is intimately related to the constraint, which selects the part of Hilbert space where the Hamilton operator is positive. This is seen as dynamical symmetry breaking in a suitably extended model, depending on a mass scale which discriminates classical dynamics beneath from emergent quantum mechanical behaviour.Comment: 8 pages, RevTeX. Based on talk at DICE2004, Piombino (Italy), September 1-4, 2004. -- To appear in Brazilian Journal of Physic