sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

The superalgebra eigenstates (SAES) concept is introduced and then applied to find SAES associated to the sh(2/2) superalgebra, also known as Heisenberg–Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2)Ð sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg–Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the super-Hermitian and -pseudo-super-Hermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.     

Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry

We present the gravitational coupling function () in the vacuum scalar-tensor theory as allowed by the Noether symmetry. We also obtain some exact cosmological solutions in the spatially homogeneous and isotropic background thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotically, the scalar tensor theory goes over to Einstein theory with a finite value of . This work thus supports earlier works in this direction.     

Coherent Solid-State Phase Transitions with Atomic Diffusion: A Thermomechanical Treatment

Using the framework of modern continuum thermomechanics, we develop sharp- and diffuse-interface theories for coherent solid-state phase transitions. These theories account for atomic diffusion and for deformation. Of essential importance in our formulation of the sharp-interface theory are a system of configurational forces and an associated configurational force balance. These forces, which are distinct from standard Newtonian forces, describe the intrinsic material structure of a body. The configurational balance, when restricted to the interface, leads to a generalization of the classical Gibbs–Thomson relation, a generalization that accounts for the orientation dependence of the interfacial energy density and also for a broad spectrum of dissipative transition kinetics. Our diffuse-interface theory involves nonstandard microforces and an associated microforce balance. These forces arise naturally from an interpretation of the atomic densities as macroscopic parameters that describe atomistic kinematics distinct from the motion of material particles. When supplemented by thermodynamically consistent constitutive relations, the microforce balance yields a generalization of the Cahn–Hilliard relation giving the chemical potentials as variational derivatives of the total free energy with respect to the atomic densities. A formal asymptotic analysis (thickness of the transition layer approaching zero) demonstrates the correspondence between versions of our theories specialized to the case of a single mobile species for situations in which the time scale for interface propagation is small compared to that for bulk diffusion. While the configurational force balance is redundant in the diffuse-interface theory, when integrated over the transition layer, the limit of this balance is the interfacial configurational force balance (i.e., generalized Gibbs–Thomson relation) of the sharp-interface theory.     

Electron states in curved quantum structures with varying radius

The influence of size and shape is investigated for quantum-dot electronic states and intra-band oscillator strengths adapting a method originally due to Stevenson. The present work solves the one-band envelope-function problem for conduction-band eigenstates in the framework of theory using general curved coordinates. The eigenstates found are subsequently employed to express intra-band oscillator strengths and emphasis is given to the dependence of oscillator strengths on quantum-dot size and shape. We finally provide four simple examples.     

Hydrodynamical Reformulation and Quantum Limit of The Barut–Zanghi Theory

One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a probabilistic fluid, we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to quantize the BZ theory: by employing this time the tensorial language, more popular in first-quantization. Quantizing the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual quantum limit of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical Weyssenhoff fluid, while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.     

Stability of symmetry breaking states in finite-size Dicke model with photon leakage

We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $〈\stackrel{?}{a}〉\ne 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.     

Quantum information entropies for an asymmetric trigonometric Rosen–Morse potential

Shannon entropy for the position and momentum eigenstates of an asymmetric trigonometric Rosen–Morse potential for the ground and first excited states is evaluated. The position and momentum information entropies and are calculated numerically. Also, it is found that is obtained analytically and increases with the potential depth and width. Some interesting features of the information entropy densities and are demonstrated graphically. The Bialynicki‐Birula–Mycielski inequality is also tested and found to hold good.     

Vortex Solutions of the Liouville Equation

The most general vortex solution of the Liouville equation (which arises in nonrelativistic Chern–Simons theory) is associated with rational functions, f(z)=P(z) Qz), where P(z) and Q(z) are both polynomials, deg P相似文献   

A noncommutative deformation of topological field theory

Cohomological Yang–Mills theory is formulated on a noncommutative differentiable four manifold through the -deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the -deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley–Eilenberg homology of noncommutative spacetime and the Chevalley–Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.     

The behaviour of eigenstates of arithmetic hyperbolic manifolds

In this paper we study some problems arising from the theory of Quantum Chaos, in the context of arithmetic hyperbolic manifolds. We show that there is no strong localization (scarring) onto totally geodesic submanifolds. Arithmetic examples are given, which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom.Supported by NSF grant DMS-9102082     

Fluctuations-Inclusive Approach to Phase Transitions in Binary Mixtures

The hierarchical reference theory of fluids (HRT) is applied to the study of the phase diagram of binary mixtures of simple fluids. This approach implements the renormalization group machinery into a liquid-state theory in order to systematically deal with the effect of long-range correlations which play a crucial role in the onset of criticality and phase separation. The effect of fluctuations is embodied in a partial differential equation (PDE) for the free energy of the mixture. Recently, a robust numerical algorithm has been developed which enabled us to integrate this PDE on a substantial density mesh even at low temperature, when the coexistence region spreads over most of the density– concentration plane.We have considered a model mixture of spherical particles interacting via a hard-core plus attractive tail potential, and adjusted the particle diameters ₁, ₂ and the strengths of the attractive interactions ₁₁, ₂₂, ₁₂ so as to mimic mixtures of simple fluids such as argon–krypton or neon–krypton. In the latter case the theory reproduces the occurrence of a minimum in the critical temperature (the so-called critical double point) and of immiscibility at high pressure. We have also studied the phase diagram of a symmetric mixture such that ₁= ₂ and ₁₁= ₂₂ as the ratio = ₁₂/ ₁₁ is varied. In particular, we find that, in agreement with the mean-field picture, by decreasing , a critical endpoint occurring at equal species concentration is turned into a tricritical point. An interesting feature of the HRT is that, whenever phase coexistence occurs, the conditions of phase equilibria are implemented by the theory itself, without any need of enforcing them a posteriori. This allows one to straightforwardly map the phase diagram and the critical lines of the mixture.     

New aspects of quantization of the Jackiw–Pi model: field–antifield formalism and noncommutativity

The so‐called Jackiw–Pi (JP) model for massive vector fields is a three‐dimensional, gauge‐invariant and parity‐preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck‐scale objects, i.e., via noncommutativity and the well‐known BV quantization. Namely, we have constructed the JP noncommutative space‐time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP's Planck‐scale framework.

     

Projective Relativity: Present Status and Outlook

We give a critical analysis of projective relativity theory. Examining Kaluza's own intention and the following development by Klein, Jordan, Pauli, Thiry, Ludwig and others, we conclude that projective relativity was abused in its own terms and much more in the case of newer higher dimensional Kaluza–Klein theories with non-Abelian gauge groups. Reviewing the projective formulation of the Jordan isomorphy theorem yields some hints how one can proceed in a different direction. We can interpret the condition not as a field equation in a 5-dimensional Riemannian space, e.g. as vacuum Einstein-Hilbert equation, but can (or should) interpret it as a geometrical object, a null-quadric. Projective aspects of quantum (field) theory are discussed under this viewpoint.     

Fokker–Planck Equation,Molecular Friction,and Molecular Dynamics for Brownian Particle Transport near External Solid Surfaces

The Fokker–Planck (FP) equation describing the dynamics of a single Brownian particle near a fixed external surface is derived using the multiple-time-scales perturbation method, previously used by Cukier and Deutch and Nienhuis in the absence of any external surfaces, and Piasecki et al. for two Brownian spheres in a hard fluid. The FP equation includes an explicit expression for the (time-independent) particle friction tensor in terms of the force autocorrelation function and equilibrium average force on the particle by the surrounding fluid and in the presence of a fixed external surface, such as an adsorbate. The scaling and perturbation analysis given here also shows that the force autocorrelation function must decay rapidly on the zeroth-order time scale ₀, which physically requires N _Kn1, where N _Kn is the Knudsen number (ratio of the length scale for fluid intermolecular interactions to the Brownian particle length scale). This restricts the theory given here to liquid systems where N _Kn1. For a specified particle configuration with respect to the external surface, equilibrium canonical molecular dynamics (MD) calculations are conducted, as shown here, in order to obtain numerical values of the friction tensor from the force autocorrelation expression. Molecular dynamics computations of the friction tensor for a single spherical particle in the absence of a fixed external surface are shown to recover Stokes' law for various types of fluid molecule–particle interaction potentials. Analytical studies of the static force correlation function also demonstrate the remarkable principle of force-time parity whereby the particle friction coefficient is nearly independent of the fluid molecule–particle interaction potential. Molecular dynamics computations of the friction tensor for a single spherical particle near a fixed external spherical surface (adsorbate) demonstrate a breakdown in continuum hydrodynamic results at close particle–surface separation distances on the order of several molecular diameters.     

HOW REYE'S CONFIGURATION HELPS IN PROVING THE BELL–KOCHEN–SPECKER THEOREM: A CURIOUS GEOMETRICAL TALE

It is shown that the 24 quantum states or rays used by Peres (J. Phys. A 24, 174-8 (1991)) to give a proof of the Bell–Kochen–Specker (BKS) theorem have a close connection with Reye's configuration, a system of twelve points and sixteen lines known to projective geometers for over a century. The interest of this observation stems from the fact that it provides a ready explanation for many of the regularities exhibited by the Peres rays and also permits a systematic construction of all possible non-coloring proofs of the BKS theorem based on these rays. An elementary exposition of the connection between the Peres rays and Reye's configuration is given, following which its applications to the BKS theorem are discussed.     

Rotating metrics admitting non-perfect fluids

In this paper an application of Newman-Janis algorithm in spherically symmetric metrics with the functions M(u,r) and e(u,r) has been discussed. After the transformation of the metric via this algorithm, these two functions M(u,r) and e(u,r) will be transformed to depend on the three variables u,r,. With these functions of three variables, all the Newman–Penrose (NP) spin coefficients, the Ricci as well as the Weyl scalars have been calculated from the Cartans structure equations. Using these NP quantities, we first give examples of rotating solutions of Einsteins field equations like Kerr–Newman, rotating Vaidya solution and rotating Vaidya–Bonnor solution. It is found that the technique developed by Wang and Wu can be used to give further examples of embedded rotating solutions, that the rotating Kerr–Newman solution can be combined smoothly with the rotating Vaidya solution to derive the Kerr–Newman–Vaidya solution, and similarly, Kerr–Newman–Vaidya–Bonnor solution of the field equations. It has also shown that the embedded universes like Kerr–Newman de Sitter, rotating Vaidya–Bonnor–de Sitter, Kerr–Newman–Vaidya–de Sitter can be derived from the general solutions with Wang–Wu function. All rotating embedded solutions derived here can be written in Kerr–Schild forms, showing the extension of Xanthopouloss theorem. It is also found that all the rotating solutions admit non-perfect fluids.     

Thermal configurations of oxygen in silicon

The central position and the infrared absorption coefficient of the 9 m band of Si samples were measured with Fourier transform infrared spectroscopy (FTIR) at temperatures from T=77 K to 775 K. The infrared absorption coefficients were corrected by considering background absorption and free carrier absorption calculated from the increased free carrier concentration and from the resistivity determined from Hall effect measurements. We found the central position of the 9 m band to shift to longer wavelengths with increasing temperature. The concentration [O_i] of interstitial oxygen is almost constant for T<600 K, but decreased rapidly for T>600 K. These results verified there are two types of thermal configurations of oxygen in silicon: The bonded Si₂O configuration with a binding energy E _b0.8 to 1.0 eV at T77 K to 600 K, and the Si₂O configuration coexists with a quasi-free interstitial oxygen (QFIO) state for T>600 K. The lattice potential barrier E _L, which retards QFIO atoms from migrating in the lattice, is estimated to be 1.5 to 1.6 eV. From these configurations the anomalous diffusivity of oxygen in silicon can be explained quite well.     

Paramagnetic Proton Nuclear Spin Relaxation Theory of Low-Symmetry Complexes for Electron Spin Quantum NumberS=

A generalization of the modified Solomon–Bloembergen–Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (Δ^ZFS_t) and a static (Δ^ZFS_s) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum numberS= , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term δ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin–lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua–metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water protonT₁NMRD profiles using both MSBM and the new theory.