Thermal Entanglement for Interacting Spin-1/2 Systems and its Quantum Criticality

In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B. PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq     

Topos-Theoretic Extension of a Modal Interpretation of Quantum Mechanics

This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value valuations are investigated. What is taken up is the modal approach based on a determinate lattice , which is a sublattice of the lattice of all quantum propositions and is determined by a quantum state e and a preferred determinate observable R. Topos-theoretic extension is made in the functor category of which base category is determined by R. Each true atom, which determines truth values, true or false, of all propositions in , generates also a multi-valued valuation function of which domain and range are and a Heyting algebra given by the subobject classifier in , respectively. All true propositions in are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier. Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed in the functor category . Here, the base category includes all ’s as subcategories. Although has a structure apparently different from , a subobject semi-classifier of gives valuations completely equivalent to those in ’s.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Time Flow in a Noncommutative Regime

We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics 44, 671). We construct the von Neumann algebra of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on depending on the state . The state defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair is a noncommutative probabilistic space and can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both the “time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability.     

Lower Bound of Minimal Time Evolution in Quantum Mechanics

We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S ², must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2×2 Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality of the polarization vector P of the evolving quantum state with the vector of the 2×2 hermitian Hamiltonians and it is shown that the Hamiltonian H can be parameterized by two independent parameters and Θ.     

CP asymmetry in $B \rightarrow \phi K_{S}$ in a general two-Higgs-doublet model with fourth-generation quarks

We discuss the time-dependent CP asymmetry of the decay in an extension of the standard model with both a two Higgs doublet and additional fourth-generation quarks. We show that, although the standard model with a two Higgs doublet and the standard model with fourth-generation quarks alone are not likely to largely change the effective from the decay , the model with both an additional Higgs doublet and fourth-generation quarks can easily account for the possible large negative value of without conflicting with other experimental constraints. In this model, additional large CP violating effects may arise from the flavor-changing Yukawa interactions between neutral Higgs bosons and the heavy fourth-generation down type quark, which can modify the QCD penguin contributions. With the constraints obtained from processes such as and , this model can lead to an effective as large as - 0.4 in the CP asymmetry of .Received: 25 March 2004, Revised: 20 April 2004, Published online: 18 June 2004     

Dilatonic Cosmology Model in the <Emphasis Type="Italic">ω</Emphasis>–<Emphasis Type="Italic">ω</Emphasis>′ Plane

In dilatonic cosmology model, we study the behavior of attractor solution in ω–ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). This is a good method which is useful to the study of classifying the dynamical dark energy models including “freezing” and “thawing” model. We find that our model belongs to “freezing” type model classified in ω–ω′ plane. We show mathematically the property of attractor solutions which correspond to ω _σ =−1, Ω _σ =1. The present values of energy density parameter , and are 0.715001, 0.284972 and 0.00002706 respectively, which meet the current observations well. Finally, we can obtain that the coupling between dilaton and matter affects the evolutive process of the Universe, but not the fate of the Universe.     

Quantum Groups GLp,q(2)- and $\mathit{SU}_{q_{1}/q_{2}}(2)$ -Invariant Bosonic Gases: A Comparative Study

We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries: GL _p,q (2) and . We establish the nature of the basic numbers which follow from these GL _p,q (2)- and -invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic and high-temperature thermo-statistical properties.     

The Invariant Eigen-Operator Method for?N?Harmonically Coupled Identical Oscillators

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of arbitrary number of coupled identical oscillators and derive their invariant eigen-operator. The results show that, (1) for the system of arbitrary number of identical harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or ; (2) the energy level gap of the system has two kinds of possibilities: one is that gap only related to ω that the frequency of oscillators; another one is that gap not only related to ω that the frequency of oscillators, but also related to the number of the coupling oscillators.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively $\mathcal{PT}$ -Symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x−ib) (an inversely linear plus linear, leading to a symmetric oscillator model), and S(x)=S _r (x)+iS _i (x) (a -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an η-weak-pseudo-Hermiticity generator are presented and a complexified -symmetric periodic-type model is used as an illustrative example.     

Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model

In this study we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological model by considering variable cosmological constant term Λ of the form: , and Λ∼ρ in the presence of strange quark matter with domain wall. The various physical aspects of the model are also discussed.     

A Negative Mass Theorem for the 2-Torus

Let M be a closed surface. For a metric g on M, denote the area element by dA and the Laplace-Beltrami operator by Δ = Δ _g . We define the Robin mass m(p) at the point to be the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off, and we define trace . This regularized trace can also be obtained by regularization of the spectral zeta function and is hence a spectral invariant which heuristically measures the total wavelength of the surface.We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This scale invariant quantity is a non-trivial analog for closed surfaces of the ADM mass for higher dimensional asymptotically flat manifolds.In this paper we show that in each conformal class for the 2-torus, there exists a metric with negative Δ-mass. From this it follows that the minimum of the Δ-mass on is negative and attained by some metric . For this minimizing metric g, one gets a sharp logarithmic Hardy-Littlewood-Sobolev inequality and an Onofri-type inequality.We remark that if the flat metric in is sufficiently long and thin then the minimizing metric g is non-flat. The proof of our result depends on analyzing the ordinary differential equation which is equivalent to h′′ = 1 − 1/h. The solutions are periodic and we need to establish quite delicate, asymptotically sharp inequalities relating the period to the maximum value. The author was supported by the National Science Foundation #DMS-0302647.     

Two-Parameter Deformed SUSY Algebra for Fibonacci Oscillators

We construct a two-parameter deformed SUSY algebra for the system of n ordinary fermions and n(q ₁,q ₂)-deformed bosons called Fibonacci oscillators with -symmetry. We then analyze the Fock space representation of the algebra constructed. We obtain the total deformed Hamiltonian and the energy levels together with their degeneracies for the system. We also consider some physical applications of the Fibonacci oscillators with -symmetry, and discuss the main reasons to consider two distinct deformation parameters.     

Conceptual Unification of Gravity and Quanta

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra on the groupoid Γ=E×G where E is the total space of the frame bundle over spacetime, and G the Lorentz group. The differential geometry, based on derivations of , is constructed. The eigenvalue equation for the Einstein operator plays the role of the generalized Einstein’s equation. The algebra , when suitably represented in a bundle of Hilbert spaces, is a von Neumann algebra ℳ of random operators representing the quantum sector of the model. The Tomita–Takesaki theorem allows us to define the dynamics of random operators which depends on the state φ. The same state defines the noncommutative probability measure (in the sense of Voiculescu’s free probability theory). Moreover, the state φ satisfies the Kubo–Martin–Schwinger (KMS) condition, and can be interpreted as describing a generalized equilibrium state. By suitably averaging elements of the algebra , one recovers the standard geometry of spacetime. We show that any act of measurement, performed at a given spacetime point, makes the model to collapse to the standard quantum mechanics (on the group G). As an example we compute the noncommutative version of the closed Friedman world model. Generalized eigenvalues of the Einstein operator produce the correct components of the energy-momentum tensor. Dynamics of random operators does not “feel” singularities.     

Improved bounds on the radius and curvature of the K$ \pi$ scalar form factor and implications to low-energy theorems

We obtain stringent bounds in the 〈r ² -c plane where these are the scalar radius and the curvature parameters of the scalar K form factor, respectively, using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point , as well as at , which we call the second Callan-Treiman point. The central values of these parameters from a recent determination are accomodated in the allowed region provided the higher loop corrections to the value of the form factor at the second Callan-Treiman point reduce the one-loop result by about 3% with . Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm² 〈r ² 0.21 fm²and 0.56 GeV^-4 c 1.47 GeV^-4and a strong correlation between them. A smaller value of shifts both bounds to lower values.     

Determination of the η and η<Superscript>′</Superscript> mixing angle from the pseudoscalar transition form factors

The possible range of the η– mixing angle is determined from the transition form factors F_ηγ(Q²) and with the help of up-to-date experimental data. For this purpose, the quark-flavor mixing scheme is adopted and the pseudoscalar transition form factors are calculated in the framework of light-cone pQCD, in which the transverse-momentum corrections and the contributions beyond the leading Fock state have been carefully taken into consideration. We construct a phenomenological expression to estimate the contributions to the form factors beyond the leading Fock state, based on their asymptotic behavior at Q²→0 and . By taking the quark-flavor mixing scheme, our results lead to , where the first error comes from the experimental uncertainty and the second error from the uncertainties of the parameters of the wavefunction. The possible intrinsic charm component in η and is discussed, and our present analysis also disfavors a large intrinsic charm component in η and , e.g. . PACS 13.40.Gp; 12.38.Bx; 14.40.Aq     

Exact Results for Topological Strings on Resolved <Emphasis Type="Italic">Y</Emphasis><Superscript><Emphasis Type="Italic"> p</Emphasis>,<Emphasis Type="Italic">q</Emphasis></Superscript> Singularities

We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y ^p,q manifolds and give rise via M-theory compactification to SU(p) gauge theories on . As an application we present a detailed study of the local case and compute open and closed genus zero Gromov-Witten invariants of the orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes. The mirror curve in this case is the spectral curve of the relativistic A ₁ Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic Y ^p,q geometries.     

Neutral pion photoproduction at high energies

A Regge model with absorptive corrections is employed in a global analysis of the world data on the reactions p p and n n for photon energies from 3 to 18GeV. In this region resonance contributions are expected to be negligible so that the available experimental information on differential cross-sections and single and double polarization observables at - t 2 GeV²allows us to determine the reaction amplitude reliably. The model amplitude is then used to predict observables for photon energies below 3GeV. A detailed comparison with recent data from the CLAS and CB-ELSA Collaborations in that energy region is presented. Furthermore, the prospects for determining the radiative decay width via the Primakoff effect from the reaction p p are explored.     

Existence and Completeness of the Wave Operators for Higher Order Differential Operators

The aim of the present paper is to study the existence and the completeness of the wave operators for elliptic operators of higher order (Schr?dinger operator) with short-range potential of the form: and other related results by using the trace class method. MSC: 2000 46N50, 47Dxx, 47F05.