Quantum—classical correspondence of the time-dependent linear potential

Using the trial-function method, the general solution of the Schrödinger equation for the time-dependent linear potential is obtained. Based on the Heisenberg correspondence principle, the solution of the classical equation of motion is derived from the quantum matrix elements.     

Analytical representation of half-width for molecular ro-vibrational lines in the case of dipole–dipole and dipole–quadrupole interactions

The analytical formula for half-width of molecular ro-vibrational lines is obtained for the case of dipole–dipole and dipole–quadrupole interactions. This formula depends on the variable parameters, which have to be determined by fitting to experimental half-widths or to half-widths calculated by semi-classical methods. The application of the analytical formula to the H₂O–H₂O, NH₃–NH₃, DCl–HCl and CO–H₂O systems is discussed.     

Quantum spectra and classical periodic orbit in the cubic billiard

Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.     

Control of excitons in a bent bunch of molecular aggregates by dipole–dipole interaction with quantum dots

The nonlocal dipole–dipole interaction is studied between excitations in chromophores forming a bunch or a tube of J-aggregates and closely spaced quantum dots (QDs). Equations describing the evolution of exciton pulses in a quasi-one-dimensional medium are derived taking into account the interaction with the transition resonant to nanoparticles. It is shown that the efficient controllable resonance energy transfer can occur in the system between QDs and an exciton pulse. The efficiency of this process significantly increases if the bunch of aggregates is deformed to bend nanoparticles round. It is shown that the interaction of permanent dipole moments of QDs and chromophores leads to the formation of a potential barrier or a well. It is found that the combined influence of these factors can be used to efficiently control the dynamics of pulses in aggregates.     

Quantum control with Lyapunov function and bang–bang solution in the optomechanics system

We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang–bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.     

Impact of quantum–classical correspondence on entanglement enhancement by single-mode squeezing

Quantum entanglement between two field modes can be achieved through the collective squeezing of the two respective modes. If single-mode squeezing is performed prior to such a two-mode squeezing, an enhancement of entanglement production can happen. Interestingly, the occurrence of this enhancement can be implicitly linked to the local classical dynamical behavior via the paradigm of quantum–classical correspondence. In particular, the entanglement generated through quantum chaos is found to be hardly enhanced by prior squeezing, since it is bounded by the saturation value of the maximally entangled Schmidt state with fixed energy. These results illustrate that entanglement enhancement via initial squeezing can serve as a useful indicator of quantum chaotic behaviour.     

Laser cooling of atoms in optical lattices including quantum statistics and dipole–dipole interactions

We develop a mean-field approach to include dipole-dipole interactions and quantum statistics in the atomic dynamics in bright and dark optical lattices including the proper spatial potentials instead of a simple δ-approximation. For classical distinguishable particles the results are even quantitatively similar to the properly scaled δ-function model. As the dominant effect bright and dark lattices exhibit opposite shifts in the lattice band energies and differ in their localisation properties as a function of density. The spatial-dependent potential allows strong modifications also in dark lattices, but the main conclusions obtained in the δ-approximation turn out to be still valid. Interestingly, important quantitative differences from the δ-model can occur as far as the effect of statistics in concerned, especially for fermions. We study the quantum statistical effects as a function of detuning and lattice well depths and identify the case of lattices with deep wells and large detunings as the preferred parameter region to observe them. Received 24 November 1999 / revised version: 24 June 1999 / Published online: 8 September 1999     

Operators’s-parameterized ordering and its classical correspondence in quantum optics theory

In reference to the Weyl ordering xmpn→(1/2)mΣι=0m(ιm)Xm-ιPnXι , where X and P are coordinate and momentum operator, respectively, this paper examines operators’s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence ((1-s)/2)(n+m)/2Hm,n((2/(1-s))～(1/2)α,(2/(1-s))～(1/2)α)→a+man,and its complementary relation αnα*m→(-i)n+m((1-s)/2)(m+n)/2:Hm,n(i(2/(1-s))～(1/2)a+,i((2/(1-s))～(1/2)a):,where H m,n is the two-variable Hermite polynomial, a, a+ are bosonic annihilation and creation operators respectively, s is a complex parameter. The s’-ordered operator power-series expansion of s-ordered operator sa+mans in terms of the two-variable Hermite polynomial is also derived. Application of operators’s-ordering formula in studying displaced-squeezed chaotic field is discussed.     

Microscopic theory of dipole–dipole interaction in ensembles of impurity atoms in a Fabry–Perot cavity

We develop a consistent quantum theory of the collective effects that take place when electromagnetic radiation interacts with a dense ensemble of impurity centers embedded in a transparent dielectric and placed in a Fabry–Perot cavity. We have calculated the spontaneous decay dynamics of an excited impurity atom as a specific example of applying the developed general theory. We analyze the dependence of the decay rate on the density of impurity centers and the sample sizes as well as on the characteristic level shifts of impurity atoms caused by the internal fields of the dielectric. We show that a cavity can affect significantly the pattern of collective processes, in particular, the lifetimes of collective states.     

On gravity’s role in the genesis of rest masses of classical fields

It is shown that in the Einstein-conformally coupled Higgs–Maxwell system with Friedman–Robertson–Walker symmetries the energy density of the Higgs field has stable local minimum only if the mean curvature of the \(t=\mathrm{const}\) hypersurfaces is less than a finite critical value \(\chi _c\), while for greater mean curvature the energy density is not bounded from below. Therefore, there are extreme gravitational situations in which even quasi-locally defined instantaneous vacuum states of the Higgs sector cannot exist, and hence one cannot at all define the rest mass of all the classical fields. On hypersurfaces with mean curvature less than \(\chi _c\) the energy density has the ‘wine bottle’ (rather than the familiar ‘Mexican hat’) shape, and the gauge field can get rest mass via the Brout–Englert–Higgs mechanism. The spacelike hypersurface with the critical mean curvature represents the moment of ‘genesis’ of rest masses.     

Molecular dynamics simulation of dielectric constant and cluster structure of liquid methanol: the role of cluster–cluster dipole correlations

A molecular dynamics simulation of liquid methanol at ambient conditions with two different three-site potential models was performed and the evaluated dielectric constant was discussed in the light of the cluster structure of the liquid. The distribution of the pair interaction energy of molecules and the cluster size distribution were calculated. An aggregation contribution to dielectric constant was defined and calculated as a function of the threshold H-bond energy using energetic criterion of H-bond. The structural information on dipole–dipole correlations of molecules incorporated in the size and structure distribution of aggregates proved to cover about 80% of the calculated dielectric constant of methanol. The other 20% should be attributed to the cluster–cluster dipole correlations.     

Quantum Vacuum and the Structure of Empty Space–Time

We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum).

     

Cosmological and Quantum Solutions of the Navier–Stokes Equations

Russian Physics Journal - It is shown that the vector Navier–Stokes equation has a variety of quantum solutions, so the scope of this equation is not limited to the field of classical...     

Correlation between Quantum Entanglement and Quantum Coherence in the Case of XY Spin Chains with the Dzyaloshinskii–Moriya Interaction

Journal of Experimental and Theoretical Physics - Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are...     

Boundary Solutions of the Quantum Yang–Baxter Equation and Solutions in Three Dimensions

Boundary solutions to the quantum Yang–Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the modified qYB equation, the latter being analogous to the modified classical Yang–Baxter (cYB) equation. We construct, for a large class of solutions r to the modified cYB equation, explicit boundary quantizations, i.e., boundary solutions to the qYB equation of the form I + tr + t²r₂ +. In the last section we list and give quantizations for all classical r-matrices in sl(3) sl(3).     

Quantum uncertainty and a counterexample of nonlocal classical “realism”

We analyze the scheme of an experiment in which, by examining suppression effects of the cross correlation of photons in a beamsplitter and by preparing squeezed states, it is proven that the phase difference of photons in Fock states cannot acquire a certain value, since, otherwise, the simultaneous existence of these two effects would be impossible. We show that this reveals an intrinsic inconsistency of the nonlocal classical interpretation of quantum mechanics on the basis of nonlocal classical “realism.”     

Improvement of spectral resolution by using the excitation dependence of dipole–dipole interaction in a dense atomic gas

We have studied the selective reflection from the interface between a dense rubidium (Rb) atomic vapor and a transparent dielectric. A remarkable narrowing of the spectrum, which can be used to improve the resolution of spectroscopy of dense media, has been demonstrated. This narrowing results from the reduction of the dipole–dipole interaction between atoms when the Rb vapor is excited by a strong pump laser. By using this technique, we have resolved the hyperfine structure of the Rb D₂ line, which is hidden by collisional broadening. PACS 32.70.Jz; 42.50.Ct; 34.80.Dp     

Singularities of classical and quantum correlations at critical points of the Lipkin–Meshkov–Glick model in bipartitions and tripartitions of spins

By using the lowest order expansion in the number of spins, we study the classical correlation (CC) and quantum correlations (QCs) between two spin subgroups of the Lipkin–Meshkov–Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartitions, we find that the CC and all the QCs are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartitions, however, the CC is still divergent but the QCs remain finite at the critical point. The present result shows that the CC is very robust but the QCs are much frangible to the environment disturbance.