Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution （a mixed state）, and the binomial distribution parameter is just equal to e^-2kt, where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.     

Dissipative tunneling

Zeitschrift für Physik B Condensed Matter - The rate of escape of a metastable state is studied in a temperature regime where quantum tunneling acts as the rate limiting process. The particle...     

Infinite Operator-Sum Representation of Density Operator for a Dissipative Cavity with Kerr Medium Derived by Virtue of Entangled State Representation

By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium to obtain density operators’ infinite operator-sum representation ρ(t)=∑ _m,n,l=0^∞ M _m,n,l ρ ₀ℳ _m,n,l ^† . It is noticeable that M _m,n,l is not Hermite conjugate to ℳ _m,n,l ^† , nevertheless the normalization ∑ _m,n,l=0^∞ℳ _n,m,l ^† M _m,n,l =1 still holds, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general superoperator theory needs modification.     

Dissipative molecular solitons

Theoretical analysis and numerical simulations of resonance interaction of laser radiation with a linear molecular chain have been performed. The regimes of switching waves and dissipative solitons, whose sizes for J-aggregates can reach nanometer range, have been demonstrated.     

Dissipative hydrodynamic oscillators

Summary Suitable transformations are used to convert the two-component Lorenz model for double-diffusion, Soret-driven convection and the laser with saturable absorber into either a Duffing oscillator equation or a system of two coupled Duffing oscillators. Then we discuss the range of parameter values where complete integration is possible.     

Dissipative hydrodynamic oscillators

Summary New theoretical predictions concerning overstability of viscoelastic fluids are given in terms of the Prandtl number and the ratio of viscoelastic relaxation to thermal diffusion times.

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Riassunto Si danno nuove previsioni teoriche che riguardano la sovrastabilità di fluidi viscoelastici nei termini del numero di Prandtl e del rapporto tra il rilassamento viscoelastico e i tempi di diffusione termica.

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Резюме Предлагаются новые теоретические предсказания, касающиеся устойчивости упруговязких жидкостей. Предложенный подход основан на числе Прандтля и отношении времени упруговязкой релаксации к времени термодиффузии.

     

Dissipative hydrodynamic oscillators

Summary The oscillatory motion of a liquid-liquid interface induced by the Marangoni effect,i.e. the variation of surface tension with the concentration of a surfactant, is described as the harmonic oscillation of the surfactant concentration at the interface. Then, at vanishing damping, threshold values and parameter regions for sustainedlongitudinal (Marangoni-Lucassen) waves are given in terms of the transport coefficients of the two liquids. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Dissipative photonic lattice solitons

We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.     

Dissipative solitons and antisolitons

Using the method of moments for dissipative optical solitons, we show that there are two disjoint sets of fixed points. These correspond to stationary solitons of the complex cubic–quintic Ginzburg–Landau equation with concave and convex phase profiles respectively. Numerical simulations confirm the predictions of the method of moments for the existence of two types of solutions which we call solitons and antisolitons. Their characteristics are distinctly different.     

Dissipative tunneling in nanosystems

A quantum dynamical problem has been analytically solved for a two-level system where localized states L ₀ and R ₀ are strongly coupled with reservoirs of local oscillations {L _n } and {R _n }. It is additionally assumed that the spectra of reservoirs are equidistant and the coupling constants are the same. It has been shown that the evolution of states L ₀ and R ₀ in recurrence cycles depends on three independent factors, which characterize exchange with the two-level system, exchange of L ₀ with {L _n } (R ₀ with {R _n }) and the phonon-induced decay of {L _n } and {R _n }. In addition to coherent oscillations with the frequency of the two-level system, Δ, and dissipative tunneling with a rate Δ²/πC ² (where C is the matrix element of the coupling of L ₀ and R ₀ with L _n and R _n ), a new regime appears where L-R transitions are induced by the partial recovery of the populations of L ₀ and R ₀ in each recurrence cycle due to synchronous transitions from reservoirs. These transitions induce repeating changes in the populations of the states of the two-level system (Loschmidt echo). The number and width of the echo components increase with the cycle number. Evolution becomes irregular because of the mixing of the contributions from pulses of the neighboring cycles, when the cycle number k exceeds the critical value k _c = π² C ². Unlike the populations, their cycle-average values remain regular at k ≫ k _c. When Δ ≪ πC ², the cycle-average populations oscillate with a frequency of ΔΩ/πC ² irrespective of mixing. The frequency of oscillations of the populations of the states {L _n } and {R _n } is approximately nΩ(Δ/2πC ²)², where Ω is the spacing between the neighboring levels of the reservoir and nΩ is the difference between the energies of the states L ₀ and L _n . The appearance of the mentioned low-frequency oscillations is due to the formation of collective states of the two-level system that are “dressed” by the reservoir. The predicted oscillations can be detected by femtosecond spectroscopy methods.     

Dissipative quantum Church-Turing theorem

We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.     

Ambiguities on the Quantization of a One-Dimensional Dissipative System with Position Depending Dissipative Coefficient

For a one-dimensional dissipative system with position depending coefficient, two constant of motion are deduce. These constants of motion bring about two Hamiltonians to describe the dynamics of same classical system. However, their quantization describe the dynamics of two completely different quantum systems. PACS numbers: 03.20.+i; 03.30.+ p; 03.65.-w     

Anomalous Dissipative Quantum Harmonic Oscillator

We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators＇ spectral density, the coordinate and momentum correlation functions decay as T^-4 arid T^-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.     

Dissipative Instability of Shock Waves

A new condition is obtained for the linear instability of a plane front of an intense shock wave in an arbitrary medium, which is determined by the finiteness of the viscosity. It is shown that the shock front instability occurs due to dissipative instability of the flow behind the front, which is analogous to the flow instability in the boundary layer. It is found that in the low-viscosity limit, one-dimensional longitudinal perturbations increase much faster than two-dimensional (corrugation) perturbations. The results are compared with the available data of experimental observation and numerical simulation of instability of shock waves. The comparison shows a better agreement between the new absolute shock instability as compared to the condition of such instability in the classical D’yakov theory disregarding viscosity.     

Dissipative structures in laminar semiconductors

A laminar electron semiconductor consisting of two branches is considered: passive (with a single-valued homogeneous current-voltage characteristic (CVC), and active (with an S-shaped overheated CVC). The self-consistent nonlinear problem is solved about seeking the dissipative structures (DS), the electron temperature strata and current filaments, that occur in the sandwich under consideration. The system bifurcation characteristics are found. The appearance of DS on the CVC of each of the branches and the specimen as a whole is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 63–70, October, 1985.The author is grateful to F. G. Bass, Yu. G. Gurevich, and V. S. Bochkov for discussing the results of the research.