An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Zonal PANS: evaluation of different treatments of the RANS–LES interface

The partially Reynolds-averaged Navier–Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is f_k whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS f_k = 1, in DNS f_k = 0 and in LES f_k takes values between 0 and 1. Three different ways of prescribing f_k are evaluated for decaying grid turbulence and fully developed channel flow: f_k = 0.4, f_k = k^3/2 _tot/? and, from its definition, f_k = k/k_tot where k_tot is the sum of the modelled, k, and resolved, k_res, turbulent kinetic energy. It is found that the f_k = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of f_k. This approach is used at RANS– LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with f_k = 1 in the unsteady RANS (URANS) region and f_k = 0.4 in the LES region. In fully developed channel flow, the RANS– LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location – and the choice of the treatment at the interface – may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity – and consequently also the modelled Reynolds shear stress – is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Bethe-Salpeter equation with the sine-Gordon interaction

An attempt is made to study the interaction Hamiltonian,H _int =Gψ ²(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit. We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n ⁶, wheren is the principal quantum number.     

Self-diffusion in liquid metals

A survey is made of all published data on self-diffusion in liquid metals and an examination is carried out on the temperature-dependence of D for studies covering a wide range of temperatures. Log D versus 1/T and D versus T represent the best data equally well, while D versus T ^1/2 and D versus T ² do not. The proper functional form is taken to be D=CT experimentally, and a simple free diffusion theory is developed from the standpoint of vibrational atom motion. An equation having no adjustable parameters results (D=k ² ? _D T/hk), in which κ is the vibrational force constant. Values calculated for D at the melting point are in good agreement with experimental values for potassium, sodium, copper and silver, but are below the measured values for lead, indium, zinc and tin.     

SU(2) q in a Hilbert space of analytic functions

The algebraSU(2) _q is realized in a Hilbert spaceH _q ² of analytic functions; the starting point is the differential realization of operators that satisfyq-algebra in a Hilbert spaceH _q. The Weyl realization ofSU(2) _q is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2×2 linear representation ofSU(2) _q is obtained as consistency conditions for couplingj1=j2=1/2 toj=0, 1; the derivation of Clebsch-Gordan coefficients is sketched and theq-generalization of the rotation matrices is included. The unitary correspondence ofH _q with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann's formalism for the rotation group as closely as possible.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

One-dimensional Anderson model with dichotomic correlation in the presence of external electric field

A one-dimensional diagonal tight binding electronic system with dichotomic correlated disorder in the presence of external d.c field is investigated. It is found numerically that the conductance distribution obeys fairly well to log-normal distribution in weak disorder strength in localized regime, which indicates validity of single parameter scaling theory in this limit. Contrary to the universal cumulant relation C ₁ = 2C ₂ in the absence of d.c. field, we demonstrated numerically that C ₁ ≫ 2C ₂ in the presence of the field in localized regime. We interpret this result as suppression of the fluctuation effects by the external field. In addition, it is obtained that the quantity NF _c , here N is the system size and F _c is the crossover field, decreases as the as the system energy E increases. Moreover, we find numerically a simple linear relation between the average logarithm of the conductance 〈ln(g)〉 and the field strength as 〈ln(g)〉 = C(N, λ)F, here C(N, λ) is a constant for particular values of N and λ, which is the Poisson parameter of the dichotomic process.     

Resonance method for IR sensing

A highly sensitive method for infrared radiation detection based on thermal resonance in an active bolometer is set forth. An active bolometer is a self-oscillating system consisting of an IR-sensitive cell in a feedback circuit of an adjustable proportional controller. The analysis of an active bolometer autonomous (dark) dynamics reveals that with a generalized gain factor A variation the system evolves from relaxation type towards oscillating and self-oscillating type. When A=A_c, where A_c is a critical value of the generalized gain factor A, the steady state loses stability through self-excited thermal oscillations. The resonance in a system weakly perturbed by IR radiation modulated at self-oscillation frequency q₀[1+exp(iω_ct)] is considered. It is shown that in a small precritical vicinity =(A−A_c)/A_c of the gain factor the amplitude of forced thermal oscillations is proportional to q₀/A_c. The D^* calculation reveals that the detection power of a passive (A=0) bolometer increases with feedback introduction by a factor of 1/||. The detection powers of feasible versions of an active bolometer are compared.     

Theory of spin diffusion in liquid-phase polymer systems

A general theory of spin diffusion in condensed media is constructed by the method of Zwanzig-Mori projection operators using the superpositional approximation to decouple the many-particle correlation functions. The spin diffusion coefficient is expressed in the form D _sp=D _tr+D _f , where D _tr is the contribution associated with translational displacements of the molecules and D _f is the contribution caused by intermolecular flip-flop processes. The expression for D _tr differs from the well-known Kubo-Green formula for the self-diffusion coefficient D _sd in that the integrand contains an additional factor P _f (t), which is the probability of the molecular spins not participating in intermolecular flip-flop transitions over the time t. A microscopic expression is obtained for D _f in the form of a time integral of the intermolecular dipole-dipole dynamic correlation functions. For liquid-phase polymer system with fairly high molecular mass the condition D _sp≫D _sd is satisfied. Zh. éksp. Teor. Fiz. 114, 538–554 (August 1998)     

多模奇相干态光场中的N-Y最小测不准态与N-H最小测不准态

本文根据新近建立的多模辐射场的广义非线性等阶高阶压缩理论,对多模奇相干态光场|Ψ,o〉_q中的N次方Y压缩、N次方H压缩、N-Y最小测不准态以及N-H最小测不准态等进行了详细研究.结果表明:1)当压缩阶数N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-Y最小测不准态;当N为奇数时,态|Ψ,o〉_q既不处于N-Y最小测不准态,也不呈现N次方Y压缩效应.2)当q & #183;N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-H最小测不准态;当q & #183;N为奇数时,态|Ψ,o〉_q既不处于N-H最小测不准态,也不呈现N次方H压缩效应.3)多模奇相干态|Ψ,o〉_q恒处于N-Y最小测不准态与恒处于N-H最小测不准态的条件明显不同,两者存在着严格的区别.     

An analytic relation for the thickness of accretion flows

We take the vertical distribution of the radial and azimuthal velocities into account in spherical coordinates, and find that the analytic relation c _s0/ν _K Θ=[(γ−1)/2γ]^1/2 is valid for both geometrically thin and thick accretion flows, where c _s0 is the sound speed on the equatorial plane, ν _K is the Keplerian velocity, Θ is the half-opening angle of the flow, and γ is the adiabatic index.

     

Slope parameter and scaling of differential cross-section of Λ-p scattering

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC ₁ +C ₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.     

How does the s(E + N) equation work? Comparisons with a modified Swain–Scott equation (E + sN) and revision of the N1 scale of solvent nucleophilicity

Modifications of the Swain–Scott equation (log k/k₀) = sn) give an equation log k₁ = (E + sN₁′); k₁ is the rate constant, E is an electrophilicity parameter, N₁′ is a solvent nucleophilicity parameter and s is an electrophile‐specific sensitivity parameter. The equation is tested using over 300 published first‐order rate constants (k₁) for decay of a range of benzhydrylium cations in various solvents, on which the published N₁ scale of solvent nucleophilicity is based (S. Minegishi, S. Kobayashi and H. Mayr, J. Am. Chem. Soc. 2004, 126, 5174–5181) using the alternative equation log k = s(E + N₁), in which s is a nucleophile‐specific parameter. The modified (E + sN₁′) equation provides a revised N₁′ scale of solvent nucleophilicity, and a more precise fit, with less than half the number of adjustable parameters. It is found that the sensitivities of the benzhydrylium cations to changes in solvent nucleophilicity decrease slightly as reactivity increases, in contrast to s(E + N) equations, which show no trends in s values. It is proposed that more reliable N scales can be defined using (E + sN), because N is determined directly from definitions, and residual errors (e.g. experimental or due to solvation effects) can be incorporated into the slope and intercept. The complex reasons for the success of equations of the type log k = s(E + N) are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

On the role of the final-state interactions in rare <Emphasis Type="Italic">B</Emphasis> decays

The effects of final-state interactions (FSI) in hadronic B decays are investigated. The model for FSI, based on Regge phenomenology of high-energy hadronic interactions, is proposed. It is shown that this model explains the pattern of phases in matrix elements of B → ππ and B → ρρ decays. These phases play an important role for CP violation in B decays. The most precise determination of the unitarity triangle angle α from B _d → ρπ decays is performed. The relation between CP asymmetries in B → Kπ decays is discussed. It is emphasized that the large-distance FSI can explain the structure of polarizations of the vector mesons in B decays and other puzzles like a very large branching ratio of the B decay to $ \bar \Xi $ \bar \Xi _c Λ _c .     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N1-A以及单个正常位与其余部分间的纠缠NL-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J1和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对NL-A,量子位L为奇数时,纠缠随杂质参数J1的变化与L=3类似,而L为偶数时纠缠随杂质参数|J1|的增加而增加.     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N_1-A以及单个正常位与其余部分间的纠缠N_L-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J₁和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N_1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对N_L-A, 量子位L为奇数时,纠缠随杂质参数J₁的变化与L=3类似,而L为偶数时纠缠随杂质参数|J₁|的增加而增加.     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

A grand superspace for unified field theories

Agrand superspace is proposed as the phase space for gauge field theories with a fixed structure groupG over a fixed space-time manifoldM. This superspace incorporatesall principal fiber bundles with these data. This phase space is the space of isomorphism classes ofall connections onall G-principal fiber bundles overM (fixedG andM). The justification for choosing this grand superspace for the phase space is that the space-time and the structure group are determinants of the physical theory, but the principal fiber bundle with the givenG andM is not. Grand superspace is studied in terms of a natural universal principal fiber bundle overM, canonically associated withM alone, and with a natural universal connection on this bundle. This bundle and its connection are universal in the sense that all connections on allG-principal fiber bundles (anyG) overM can be recovered from this universal bundle and its universal connection by a canonical construction. WhenG is Abelian, grand superspace is shown to be an Abelian group. Various subspaces of grand superspace consisting of the isomorphism classes of flat connections and of Yang-Mills connections are also discussed.