Non-Gaussian noise in quantum spin glasses and interacting two-level systems

We study a general model for non-Gaussian 1/f noise based on an infinite range quantum Ising spin system in the paramagnetic state, or, equivalently, interacting two-level classical fluctuators. We identify a dilatation interaction term in the dynamics which survives the thermodynamic limit and circumvents the central limit theorem to produce non-Gaussian noise even when the equilibrium distribution is that of noninteracting spins. The resulting second spectrum ("noise of the noise") itself has a universal 1/f form which we analyze within a dynamical mean-field approximation.     

Microscopic derivation of kinetic equations for interacting optical two-level systems

Kinetic equations are derived for optical two-level atoms interacting with a molecular subsystem treated as a thermostat. It is assumed that the kinetics is determined by the electric dipole interaction perturbed by the thermal motion. Dynamic parts of the kinetic equations coincide with the corresponding terms of optical Bloch equations, whereas nonlinear relaxation and shift terms have the specific form and are absent in the phenomenological generalized Bloch equations. It is shown that the relaxation kinetics can be substantially different from the exponential one and depends on the initial state of the system. In particular, the inversion relaxation is frozen at small deviations from the equilibrium. The possibility of observation of the optical bistability is discussed.     

Duality between the weak and strong interaction limits for randomly interacting fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U= infinity eigenstates bases, respectively. This implies the existence of a duality point U(d) where the eigenstates have the same spreading in both bases. U(d) is surrounded by an interval of finite width which is characterized by a non-Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.     

Electron phonon systems from weak to strong coupling

Electron and phonon spectra are derived for an electron-phonon system coupled by the Fröhlich interaction. We cover the range from small coupling <1 to large coupling 1 for a commensurate filling of the bare band. The evolution of the Migdal solution into a charge density wave and finally into a regular lattice of small polarons is studied.     

Modified optical bloch equations in nonlocal systems of two-level atoms interacting with ultrashort light pulses

Modified optical Bloch equations for two-level atoms in the radiation field with the complex polarization vector, the complex amplitude, and the complex wave vector are derived. A specific case is considered in which a field of this kind acts on a separate atom of a nonlocal atomic system. The solution of the modified equations for the interaction of atoms with ultrashort light pulses is obtained.     

Pairing correlations in finite systems: from the weak to the strong fluctuations regime

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.     

Theory of absorption and amplification spectra of a weak electromagnetic field by two-level quantum systems

A theory is developed of the absorption and amplification spectra of a weak (probe) electromagnetic field (EMF) by open two-level quantum systems in a strong quasiresonant EMF, assuming separability of the triplet spectrum components. The theory describes the intensity and the form of the spectral lines for arbitrary intensities and detunings of the strong EMF, and also the dependence of the parameters of the adiabatic relaxation on the frequency of the weak EMF. The influence of nonlinear dynamic effects (NDE) due to the dependence of the relaxation on the EMF parameters on the shape of the spectral lines is investigated. It is shown, in particular, that under certain conditions the NDE can lead to a nonlinear dynamic transformation of the dispersion of the sideband dispersion lines into Lorentzian lines and to a considerable increase of the absorption in the central region of the spectrum. Particular attention is paid to an investigation of the NDE on the characteristics of the central component of the spectrum. Methods and results of an investigation of the spectra in a basis of unperturbed wave functions in in a basis of dressed states are compared.Radiophysics Division, Lebedev Physics Institute. Translated from Preprint No. 117 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.     

Information and two-level systems

I consider the general functions depending on the quantum state represented by a two-level density matrix. Quantities of relevance are state distance and informations measures, i.e. entropies. I introduce a new complex representation of such functions. Utilizing the geometric interpretation of complex mappings, I summarize several properties of such transformations of the state. In particular these results are used to suggest several possible applications to physical questions. These are tentative only, but they indicate the physical relevance of the mathematical results presented.     

For 2-D lattice spin systems weak mixing implies strong mixing

We prove that for finite range discrete spin systems on the two dimensional latticeZ ², the (weak) mixing condition which follows, for instance, from the Dobrushin-Shlosman uniqueness condition for the Gibbs state implies a stronger mixing property of the Gibbs state, similar to the Dobrushin-Shlosman complete analyticity condition, but restricted to all squares in the lattice, or, more generally, to all sets multiple of a large enough square. The key observation leading to the proof is that a change in the boundary conditions cannot propagate either in the bulk, because of the weak mixing condition, or along the boundary because it is one dimensional. As a consequence we obtain for ferromagnetic Ising-type systems proofs that several nice properties hold arbitrarily close to the critical temperature; these properties include the existence of a convergent cluster expansion and uniform boundedness of the logarithmic Sobolev constant and rapid convergence to equilibrium of the associated Glauber dynamics on nice subsets ofZ ², including the full lattice.Work partially supported by grant SC1-CT91-0695 of the Commission of European Communities and by grant DMS 91-00725 of the American NSF.     

Supersymmetry of two-level systems

Physics Institute, Russian Academy of Sciences. Presented at the International Workshop Squeezing, Groups, and Quantum Mechanics, Baku, Azerbaijan, September 16–22, 1991.     

Calculation and analysis for acoustic radiation mode of strong and weak plate-cavity coupling systems

A method based on the energy principle is proposed for calculating the acoustic radiation mode of plate-cavity coupling systems.The relationship between the acoustic pressure mode amplitude vector and the structural mode amplitude vector is constructed according to the kinetics equations based on the energy principle.The acoustic radiation mode of plate-cavity coupling systems is derived by expressing the acoustic potential energy as a quadratic form of the structural mode amplitude vector.The p...     

Simulation of two-level systems

A macroscopic model of a two-level system that contains only classical components but reproduces quantum states is constructed using numerical methods. A computer analog of the measuring procedure is developed. The analysis of the single-particle state distribution makes it possible to compare the results with quantum mechanical results. In the modeling of a two-particle singlet state, the probability and correlation functions distributions and restrictions on the Bell??s parameters are obtained. The results agree with the quantum-mechanical results.     

对称强双色共振场中弛豫效应对二能级系统斯塔克分裂的影响

本文应用半径典理论、密度矩阵方法和探索场中二能级系统的能级斯塔克(Stark)分裂。指出与无弛豫效应相比较,弛予效应不仅改变了由光学斯塔克效应所产生的分裂能级的权重、展宽了这些能级,而且还出现新的分裂能级。     

Dipole relaxation in weak and strong fields

The process of dipole relaxation in a homogeneous dielectric is studied on the basis of a two-state dipole model. The external field is not assumed to be weak. Two types of applied electric fields are considered: a linearly increasing field, and a field which changes by steps. At the present time pulsed electric fields have found wide application in electron-ion technology.Translated from Izvestiya VUZ. Fizika, No. 1, pp. 95–100, January, 1972.     

Coherence loss of large fields interacting with two-level atoms

Preliminary results are reported on the coherence properties of a large and initially coherent e.m. field interacting with a set of resonant two-level atoms. The field is shown to behave non-classically relatively large times, since its variance increases linearly with time.     

Relaxation in two-level long-range-memory systems

Recently, new rigorous results concerning integrals of exact memory functions in the time-convolution Generalized Master Equations (GME) for state occupation probabilities, governing relaxation of open quantum systems, have been obtained. They include that a) time integrals of exact memories and b) memories w _ij(t) have tails unobtainable by perturbational arguments which cause that does not exist or is infinite. For a two-level system, a simple model for such memories is considered and solved. It is concluded that GME may yield that with increasing time, the system unphysically more and more deviates from equilibrium, indicating thus instability of the equilibrium distribution. Thus, in contrast to, e.g., the famous Boltzmann equation, the mathematical structure of GME alone does not guarantee the stability of the equilibrium state.