Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.     

Critical Properties of a Quantum Hierarchical Model

A model of hierarchically interacting quantum anharmonic oscillators is considered. For this model, the sequence of abnormally normed fluctuations of the coordinate operator is shown to converge to a nontrivial thermodynamic limit when the model parameters satisfy certain conditions. This is a manifestation of the presence of a critical point for the model. Conditions on the parameters are also found which are sufficient to exclude critical points.     

Uniqueness Problem for Quantum Lattice Systems with Compact Spins

Quantum lattice systems with compact spins and nearest-neighbour interactions are considered. Uniqueness of the corresponding Euclidean Gibbs states is proved uniformly with respect to the temperature, in the case where the particles have a sufficiently small mass.     

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on a lattice ^d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;² tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with pair interactions possessing the translation invariance, has also been shown.     

Spherical Model in a Random Field

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r ^4−d .     

Arithmetic of the Integer Quantum Hall Effect

The integer quantum Hall effect (IQHE) is analysed, considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted, and their variation is studied as a function of magnetic field. The number of current-carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis addresses certain basic questions in the IQHE, particularly the one about floatation of extended states as the magnetic field tends to zero.     

Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently.The authors [Phys.Rev.A 88(2013) 034304] found that for some Bell-diagonal states(BDS)which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics,this phenomenon is known as the sudden change.Here in the present paper,we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs.Then,we find that basis change does not necessary mean sudden change of quantum correlations.     

Dynamics of a Ring of Diffusively Coupled Lorenz Oscillators

We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a stable fixed state in arbitrarily large rings for a fixed coupling strength. This suggests that coherent behavior in networks of diffusively coupled systems may appear at a coupling strength that is independent of the size of the network.     

频率变化场J-C模型中的量子态保真度

利用Jaynes-Cummings模型,考虑场频率受微扰的情况,在旋波近似下研究了二能级原子与单模辐射场相互作用系统中量子态保真度的演化.利用数值计算方法给出量子态保真度随时间的演化曲线.研究了场频率随时间正弦函数形式变化对系统、光场和原子的量子态保真度演化的影响.结果表明:场频率随时间正弦函数形式变化对系统和光场的量子态保真度的演化的影响很小,但对原子的量子态保真度的演化有显著影响.     

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature T_c of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, T_c decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect T_c. This implies that the hubs play an important role in maintaining order in the whole network.     

LRO in Lattice Systems of Linear Classical and Quantum Oscillators. Strong Nearest-Neighbor Pair Quadratic Interaction

For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour translation invariant term, an existence of a ferromagnetic long-range order for two valued lattice spins, equal to a sign of oscillator variables, is established for sufficiently large magnitude g of the n-n interaction with the help of the Peierls type contour bound. The Ruelle superstability bound is used for a derivation of the contour bound.     

Anharmonic resonances in the vibrational spectra of pyrazine

The quartic force field of pyrazine has been calculated in the B3LYP/6-31G(d) hybrid density-functional approximation. Based on the results of this calculation, the total IR (250–3800 cm^–1) and Raman (400–3200 cm^–1) spectra of pyrazine have been interpreted with consideration for the Fermi and Darling-Dennison resonances and their spectral manifestations. A precision method is proposed for anharmonic analysis of the vibrational states of polyatomic molecules on the basis of consideration of their theoretical anharmonicity constants in combination with the corresponding experimental frequencies. The method of linear scaling of frequencies has been theoretically substantiated.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 13–22, January–February, 2005.     

双模环型激光增益噪声模型的非线性效应

讨论了一个双模环型激光增益噪声模型，其中考虑了完全饱和效应且乘法噪声由增益系数涨落引起。在共振及两模具有相同泵参数时，获得了光强联合定态分布的精确解析表达式。通过与现有的双模激光摸型（其中乘法噪声由损失系数涨落引起）的比较，发现乘法噪声系数的非线性效应减弱了乘法噪声给激光光强统计性质带来的反常特性，并且这种减弱随着乘法噪声增强或损失系数减小而愈加明显。     

Effects of Impurity on the Ground—State Transitions of a Quantum Dot in Strong Magnetic Field

The low-lying spectra of parabolic quantum dots with or without an impurity at the center are investigated.While it has been known that the electron-electron interaction leads to ground-state transitions on magic values of angular momentum in a magnetic field.We show,in this paper,that the implantation of an impurity ion at the center can either enhance or suppress such transitions,depending on whether it is an acceptor or a donor ion.     

Excluded Volume Effects for Frequency Moments of the Spin Autocorrelation Function of the Heisenberg Model on a Square Lattice at High Temperatures

The expansion coefficients in powers of time (or frequency moments) of the spin autocorrelation function are represented at the simple self-consistent approximation as a sum of weighted trees on a Bethe lattice. Using the computer numeration and the Monte Carlo method for self-avoidingly embedding these trees on the square lattice, we estimate the moments and the convergence radius of the expansion. We show that the moments decrease and the radius increases in consequence of the volume exclusion.     

Hyperspherical Analysis of D- in a Quantum Well

By introducing hyperspherical coordinates and assuming the quasiseparability of the hyperradius R from the angular variables Ω in the wavefunctions, we have solved the SchrSdinger equation for a D- center in two dimensions to obtain the low-lying spectrum. The correlation patterns in these states are visualized.``     

Quantum Superposition of Two Coherent States in a Mesoscopic Josephson Junction

We study a mesoscopic Josephson junction in a circular superconducting ring which encloses a magneto static flux. It is shown that with the junction being initially prepared in vacuum state, the state of the junction can evolve into a quantum superposition of two coherent states.