Real and Complex Analysis

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of such systems acts on the resolvent algebra by automorphisms and there exists a (in any regular representation) weakly dense subalgebra on which this action is pointwise norm continuous. Based on this observation, equilibrium (KMS) states as well as ground states are constructed, which are shown to be regular. It is also indicated how to deal with singular interactions and non-harmonic oscillations.

The Resolvent Algebra for Oscillating Lattice Systems: Dynamics, Ground and Equilibrium States

Non-equilibrium steady states, in the sense of Ruelle [Commun. Math. Phys. 224, 3–16 (2001)], of Boson systems with Bose–Einstein condensation are investigated with the aid of the C*-algebraic method. The model consists of a quantum particle and several bosonic reservoirs. We show that the mean entropy production rate is strictly positive and independent of phase differences provided that the temperatures or the chemical potentials of reservoirs are different. Moreover, Josephson currents occur without entropy production, if the temperatures and the chemical potentials of reservoirs are identical.Non-equilibrium steady states, in the sense of Ruelle [Commun. Math. Phys. 224, 3–16 (2001)], of Boson systems with Bose–Einstein condensation are investigated with the aid of the C*-algebraic method. The model consists of a quantum particle and several bosonic reservoirs. We show that the mean entropy production rate is strictly positive and independent of phase differences provided that the temperatures or the chemical potentials of reservoirs are different. Moreover, Josephson currents occur without entropy production, if the temperatures and the chemical potentials of reservoirs are identical.

A model of Josephson junctions on Boson systems—Currents and entropy production rate

Non-equilibrium steady states (NESS), in the sense of D. Ruelle, of Boson systems with Bose--Einstein condensation (BEC) are investigated with the aid of the C^*-algebraic method. The model consists of a quantum particle and several bosonic reservoirs. We show that the mean entropy production rate is strictly positive, independent of phase differences provided that the temperatures or the chemical potentials of reservoirs are different. Moreover, Josephson currents occur without entropy production, if the temperatures and the chemical potentials of reservoirs are identical.

A model of Josephson Junctions on Boson Systems - Currents and Entropy Production Rate -

The virtues of resolvent algebras, compared to other approaches for the treatment of canonical quantum systems, are exemplified by infinite systems of non-relativistic bosons. Within this framework, equilibrium states of trapped and untrapped bosons are defined on a fixed C*-algebra for all physically meaningful values of the temperature and chemical potential. Moreover, the algebra provides the tools for their analysis without having to rely on 'ad hoc' prescriptions for the test of pertinent features, such as the appearance of Bose-Einstein condensates. The method is illustrated in case of non-interacting systems in any number of spatial dimensions and sheds new light on the appearance of condensates. Yet the framework also covers interactions and thus provides a universal basis for the analysis of bosonic systems.

Trapped bosons, thermodynamic limit and condensation: a study in the framework of resolvent algebras

We consider equilibrium states of weakly coupled anharmonic quantum oscillators(= anharmonic crystal) on an integer lattice \(\mathbf{Z}\). We employed standard functional analytic methods for Schrodinger operators and we show existence of the infinite volume limit of equilibrium states, and uniqueness of the regular KMS (Kubo–Martin–Schwinger) states in the frame of Resolvent CCR Algebra introduced by D. Buchholz and H. Grundling.

Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra

We consider Bose–Einstein condensation (BEC) on graphs with transient adjacency matrix. We prove the equivalence of BEC and non-factoriality of the quasi-free state. Moreover, quasi-free states exhibiting BEC decompose into generalized coherent states. We review necessary and sufficient conditions that a quasi-free state is faithful, factor, and pure and quasi-free states are quasi-equivalent, including the papers of Araki and Shiraishi [1], Araki [2], and Araki and Yamagami [3]. Using their formats and results, we prove necessary and sufficient conditions that a generalized coherent state is faithful, factor, and pure and generalized coherent states are quasi-equivalent as well.

/pdf/remarks-on-bec-on-graphs-4gli81f0m6.pdf

Remarks on BEC on graphs

Non-equilibrium steady states (NESS) of Boson systems with different phases are investigated with the aid of the C^*-algebraic method The system consists of sample and several free or pure-hopping bosonic reservoirs coupled with each other Initially, the sample and reservoirs are uncoupled and in equilibrium with temperatures, local densities, and phases At t=0, the reservoirs couple with each other through the sample NESS are constructed as time limit of the composition of initial state and time evolution of coupled system In NESS, Josephson currents and the mean entropy production rates are calculated The mean entropy production rate does not depend on phase differences As consequence, the currents provided to phase differences produces no entropy

Non-equilibrium steady states for a Harmonic oscillator interacting with several Boson systems - Currents and Entropy production rate -

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