Global C*-Dynamics and Its KMS States of Weakly Inhomogeneous Bipolaronic Superconductors

We establish the limiting dynamics of a class of inhomogeneous bipolaronic models for superconductivity which incorporate deviations from the homogeneous models strong enough to require disjoint representations. The models are of the Hubbard type and the thermodynamics of their homogeneous part has been already elaborated by the authors. Now the dynamics of the systems is evaluated in terms of a generalized perturbation theory and leads to a C*-dynamical system over a classically extended algebra of observables. The classical part of the dynamical system, expressed by a set of 15 nonlinear differential equations, is observed to be independent from the perturbations. The KMS states of the C*-dynamical system are determined on the state space of the extended algebra of observables. The subsimplices of KMS states with unbroken symmetries are investigated and used to define the type of a phase. The KMS phase diagrams are worked out explicitly and compared with the thermodynamic phase structures obtained in the preceding works.     

Minimal Coupling in Koopman-von Neumann Theory

Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 1930s. They basically formalized, via the introduction of a classical Hilbert space, earlier work of Liouville who had shown that the classical time evolution can take place via an operator, nowadays known as the Liouville operator. In this paper we study how to perform the coupling of a point particle to a gauge field in the KvN version of CM. So we basically implement at the classical operatorial level the analog of the minimal coupling of QM. We show that, differently than in QM, not only the momenta but also other variables have to be coupled to the gauge field. We also analyze in detail how the gauge invariance manifests itself in the Hilbert space of KvN and indicate the differences with QM. As an application of the KvN method we study the Landau problem proving that there are many more degeneracies at the classical operatorial level than at the quantum one. As a second example we go through the Aharonov-Bohm phenomenon showing that, at the quantum level, this phenomenon manifests its effects on the spectrum of the quantum Hamiltonian while at the classical level there is no effect whatsoever on the spectrum of the Liouville operator.     

Minimal Coupling Method and the Dissipative Scalar Field Theory

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field is investigated by it's coupling to an infinite number of Klein–Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to the velocity is obtained for a special choice of coupling function and quantum dynamics for such a dissipative system is investigated. Some kinematical relations is calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment is obtained.     

Comparison of methods for determination of viscoelastic properties in chiral smectics C*

The knowledge of the material parameters related to the microscopic structure of liquid crystals is one of the main problems in the construction of the liquid crystal devices. In the case of ferroelectric liquid crystals, the viscoelastic properties are very important as they determine the switching speed and the threshold voltage in displays. There exist several experimental methods for measurements of viscosity and elasticity constants in tilted smectic phases which exploit various phenomena for deformation detection, e.g., light transmission, polarization current, light modulation, dielectric constant, and helix deformation or helix unwinding. In this article, we compared the results of measurements obtained for the same material using various methods. The experiments proved that the correct bulk values of the mentioned material constants can be determined using thick, homeotropically aligned samples only.     

Solution of the Dipoles in Noncommutative Space with Minimal Length *

The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative (NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.     

C*-algebras and Mackey's axioms

A non-commutative version of probability theory is outlined, based on the concept of a*-algebra of operators (sequentially weakly closedC*-algebra of operators). Using the theory of*-algebras, we relate theC*-algebra approach to quantum mechanics as developed byKadison with the probabilistic approach to quantum mechanics as axiomatized byMackey. The*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by theW*-algebra approach. By considering the*-algebra, rather than the von Neumann algebra, generated by the givenC*-algebraA in its reduced atomic representation, we show that a difficulty encountered byGuenin concerning the domain of a state can be resolved.     

C*-algebras and automorphism groups

Let (A,G, α) be aC*-dynamical system withG a topological group. Let π be a representation ofA. We will show that there exists a quasiequivalent representation \(\hat \pi \) to π which is a covariant representation, if and only if the folium of π is invariant under the action ofG and this action is strongly continuous.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

Unbounded derivations of C*-algebras

We study unbounded derivations ofC*-algebras and characterize those which generate one-parameter groups of automorphisms. We also develop a functional calculus for the domains of closed derivations and develop criteria for closeability. Some specialC*-algebras are considered \(\mathfrak{B}\mathbb{C}(\mathfrak{H}),\mathfrak{B}(\mathfrak{H})\) , UHF algebras, and in this last context we prove the existence of non-closeable derivations.     

Smooth (C2) formation of a persistent naked singularity

We construct a smooth (C²) transition from Minkowski space to Schwarzchild space by way of an ingoing Vaidya field in a finite interval of advanced time. This transition results in a persistent globally naked singularity.     

Some Examples of Graded C*-Algebras

We apply the theory of C*-algebras graded by a semilattice to crossed products of C*-algebras. We establish a correspondence between the spectrum of commutative graded C*-algebras and the spectrum of their components. This will allow us to compute the spectrum of some commutative examples of graded C*-algebras.     

Quasi-Product Flows on a C*-Algebra

 A version of Glimm's theorem is given for a flow on a separable C^*-algebra; i.e., we give necessary and sufficient conditions for the flow under which any UHF flow (product type flow on a UHF algebra) is embedded in an inner perturbation of the flow. Received: 5 February 2002 / Accepted: 22 March 2002 Published online: 12 August 2002     

Defects in smectic C* liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C* liquid crystals. The polarization field associated with disclinations, the effect of incommensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

严格耦合波理论和Kogelnik耦合波理论近似比较

将严格耦合波理论与Kogelnik近似理论比较,研究了Kogelnik理论的近似条件。以两种理论的衍射效率特性曲线的相关或衍射效率计算差别作为判断标准,分析Kogelnik耦合波理论的近似条件。分析结论表明,体全息的Kogelnik理论近似条件与条纹密度、折射率调制度和介质厚度相关,其中反射体全息的近似条件还与条纹面倾角相关。