Long time properties of the evolution of an unstable state

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as t → ∞ more slowly than any exponential function of t. This can be described in terms of the time-dependent decay rate γ(t) which, when considered with the Khalfin result, means that this γ(t) is not a constant for large t but that it tends to zero as t → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which can be interpreted as the “instantaneous energy” of the unstable state. This energy should be much smaller for suitably larger values of t than when t is of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long (t → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.      

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

System-parameter dependence of the metallic phase of the non-doped 2D Hubbard model

Naito et al. reported that some non-doped T′-214-type compounds drive high-T_c superconductivity. The compounds are considered to be metallic since on-site Coulomb energy U is moderate and the Fermi surface is much deformed in these compounds. In order to confirm this picture and extract electronic structure information, we have examined the phase diagram of the metallic state of the 2D Hubbard model as a function of U and t′ (with t″ we fixed at − t′/2 here; t′ and t″ are the second- and third-neighbor transfer energies, respectively) by means of the variational Monte–Carlo method. We employed a Jastrow-type Gutzwiller trial wave function. In the studied range of U = 2–12, the boundary value for |t′| at which SDW disappears increases almost linearly with U. Jump-wise transition to the Mott insulator state was not observed. Using the boundary curve and experimental band parameter values, we estimate U  5 for T′-214 compounds. Preceding works are discussed in the last part.     

Higher-Order Nonclassicality in Photon Added and Subtracted Qudit States

Higher-order nonclassical properties of r photon added and t photon subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are investigated here to answer: How addition and subtraction of photon can be used to engineer higher-order nonclassical properties of qudit states? To obtain the answer, higher-order moment of relevant bosonic field operators is first obtained and subsequently used to study the higher-order nonclassical properties (e.g., higher-order antibunching, higher-order squeezing, and higher-order sub-Poissonian photon statistics) of the corresponding states. These witnesses establish that rPAQS and tPSQS are highly nonclassical. To quantitatively establish this observation and to make a comparison between rPAQS and tPSQS, volumes of the negative part of Wigner function are computed. Finally, for the sake of verifiability of the obtained results, optical tomograms are also reported. Throughout the study, a particular type of qudit state named as a new generalized binomial state is used as an example.     

Spreading of wave packets in the Anderson model on the Bethe Lattice

The spreading of wave packets evolving under the Anderson Hamiltonian on the Bethe Lattice is studied for small disorder. The mean square distance travelled by a particle in a timet is shown to grow ast ² for larget.The author was supported in part by the NSF Grant DMS-9208029.     

Remark on state vector construction when flavor mixing exists

In the framework of quantum field theory, we consider the way to construct the one-particle state (with definite 3-momentum) when particle mixing exists, such as in the case of flavor-neutrino mixing. In the preceding report (Prog. Theor. Phys. 112, 901 (2004)), we have examined the structure of expectation values of the flavor neutrino charges (at time t) with respect to a neutrino-source state prepared at time t′ (earlier than t). When there is no mixing, each of various contributions to the expectation value is equal, in its dominant part, to the transition probability corresponding to the respective neutrino-production process. On the basis of the assumption that such an equality holds also in the mixing case, we can find an appropriate form of one-flavor-neutrino state with 3-momentum and helicity. Along the same way, we examine the boson case when flavor mixing exists. We give remarks on the relation and difference between the ordinary and the present approaches to flavor oscillation. The text was submitted by the authors in English.     

On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents

For Hamiltonian systems subject to an external potential which in the presence of a thermostat will reach a nonequilibrium stationary state Dettmann and Morriss proved a strong conjugate pairing rule (SCPR) for pairs of Lyapunov exponents in the case of isokinetic (IK) stationary states which have a given kinetic energy. This SCPR holds for all initial phases of the system, all times t, and all numbers of particles N. This proof was generalized by Wojtkowski and Liverani to include hard interparticle potentials. A geometrical reformulation of those results is presented. The present paper proves numerically, using periodic orbits for the Lorentz gas, that SCPR cannot hold for isoenergetic (IE) stationary states which have a given total internal energy. In that case strong evidence is obtained for CPR to hold for large N and t, where it can be conjectured that the larger N, the smaller t will be. This suffices for statistical mechanics.     

Deuteron form factors and the tensor force

Results of a non-relativistic calculation of deuteron form factors are presented for separable potentials with and without tensor force. The tensor term in triplet state is added in such a way as to keep the values of deuteron binding energy,a _t andr _0t unaltered, so that the difference in the form factors can be regarded as the effect of tensor force only. The calculation has been performed for two different shapes of separable potentials and for three differentD-state probabilities to study their comparative effect.     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

Rotational structure of the origin band in the 1A′ ←X1σ+ electronic transition of C4H− and C4D−

The rotational structure of the origin band for the ¹A′←X¹σt⁺ electronic transition, lying just below the electron affinity of C⁴H, was recorded by means of a two-colour resonant photodetachment technique. This allowed a determination of the rotational constants in the X¹σt⁺ ground and ¹A′ dipole bound excited state. The low lying A²II excited state of C⁴H is inferred to be the parent of the dipole bound state. The excited electronic state is deduced to have a nonlinear planar structure whereas the ground is linear according to the spectral analysis. The rotational constants have been obtained: B′; = 0.1552(2)cm^?1 for the X¹σt⁺ state, and A′ = 30.73(1), B′ = 0.1587(2), C′ = 0.1581(2)cm^?1 for the ¹A′ state.     

Optical control of the coherent dynamics of excitons in a semiconductor quantum well

The dynamics of the coherent superposition of exciton states in a semiconductor quantum well excited by the joint action of two successive light pulses with the time interval between them t ₁₂ has been theoretically studied. The dependences of the amplitude and initial phase of the quantum bits on t ₁₂ have been found. It has been shown that the time dependence of the Kerr rotation of the reflected probe pulse is determined not only by the dynamics of the excited state, but also by the optical properties of the heterostructure containing the quantum well. The dependence of the decay rate of the excited state on t ₁₂ has been predicted.     

Viscous dark cosmology with account of quantum effects

The analytic properties of the energy density ρ(t) of the cosmic fluid and the Hubble parameter H(t) are investigated close to the future singularity t=t _s assuming different forms for the equation of state. First, it is shown that the inclusion of quantum effects coming from the conformal anomaly modifies the singularity. Thereafter, we consider the effect coming from the bulk viscosity in the fluid. The viscosity tends to reduce the magnitude of t _s, but does not alter the singularity itself (the exponent). The main emphasis is laid on the simple case when the equation of state is p=w ρ, with w a constant.     

Evolution of a Model Quantum System¶ Under Time Periodic Forcing:¶Conditions for Complete Ionization

We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation η(t). We show that for generic η(t), which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized as t→∞. This is irrespective of the magnitude or frequency (resonant or not) of η(t). There are however exceptional, very non-generic η(t), that do not lead to full ionization, which include rather simple explicit periodic functions. For these η(t) the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator. Received: 1 November 2000 / Accepted: 5 February 2001     

On the short-time behaviour of quantum unstable systems

We consider the survival amplitudeA(t) for a normalized decaying state whose energy spectral density vanishes asymptotically as an inverse power. By using simple calculus a Taylor expansion ofA(t) is derived aroundt=0, the form of the remainder term identified, and a physical significance given to the other coefficients. It is shown that the Taylor remainder may contain logarithms oft besides powers.     

Rheological Technique as a Sensitive Method to Characterize the Chain Diffusion across the Interface between Polystyrene and Carbon Black Filled Polystyrene

The mutual diffusion process and interphase development taking place at the interface between disks of polystyrene (PS) and carbon black filled polystyrene (CB-PS) in the molten state were investigated by a small-amplitude, oscillatory shear, rheological technique. The rheological method was employed to probe the thermorheological complexity of these polymer disks. It was found that the dynamic complex shear modulus, G*(t), increased with the time of contact in two time regimes at a fixed frequency. The time of transition between the two regimes was observed to be close to the time needed for the transition from the Rouse mode to the reptation mode. The results showed that the content of the carbon black and the temperature affected the slope of the G*(t) – t curve. Scanning electron microscopy revealed the interface disappeared when the diffusion process was complete.     

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-T_c superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C_4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C_4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t₁/t₀, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states.     

Multichannel nonlinear scattering for nonintegrable equations

We consider a class of nonlinear Schrödinger equations (conservative and dispersive systems) with localized and dispersive solutions. We obtain a class of initial conditions, for which the asymptotic behavior (t±) of solutions is given by a linear combination of nonlinear bound state (time periodic and spatially localized solution) of the equation and a purely dispersive part (decaying to zero with time at the free dispersion rate). We also obtain a result ofasymptotic stability type: given data near a nonlinear bound state of the system, there is a nonlinear bound state of nearby energy and phase, such that the difference between the solution (adjusted by a phase) and the latter disperses to zero. It turns out that in general, the time-period (and energy) of the localized part is different fort+ from that fort–. Moreover the solution acquires an extra constant asymptotic phasee ^{iy ±}.This research was supported in part by grants from the National Science FoundationThe results of this paper were announced in a lecture (June, 1988) on which the Proceedings article [Sof-We] is based     

A quantum long time energy red shift: a contribution to varying <Emphasis Type="Italic">α</Emphasis> theories

By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in the long (t→∞) and relatively short (lifetime of the state) time regions are different. It is shown that in the considered model the above corrections decrease to zero as t→∞. It is hypothesized that this property could be detected by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of possible deviations of the fine structure constant α as well as other astrophysical and cosmological parameters.