Dissipationless Case Research Articles

Logical and thermodynamical reversibility: Optimized experimental implementation of the not operation.

The not operation is a reversible transformation acting on a 1-bit logical state and should be achievable in a physically reversible manner at no energetic cost. We experimentally demonstrate a bit-flip protocol based on the momentum of an underdamped oscillator confined in a double-well potential. The protocol is designed to be reversible in the ideal dissipationless case, and the thermodynamic work required is inversely proportional to the quality factor of the system. Our implementation demonstrates an energy dissipation significantly lower than the minimal cost of information processing in logically irreversible operations. It is, moreover, performed at high speed: A fully equilibrated final state is reached in only half a period of the oscillator. The results are supported by an analytical model that takes into account the presence of irreversibility. This Research Letter concludes with a discussion of optimization strategies.

Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.

Nonlinear dynamics of driven superconductors with dissipation

We study the out-of-equilibrium dynamics of a BCS superconductor in the presence of a periodic drive with a frequency $\omega_d$ larger than the equilibrium superconducting gap and an external bath providing dissipation. Similar to the dissipationless case, a subset of quasiparticles, resonant with the drive, synchronizes and produces interesting non-linear phenomena. For small dissipation Rabi-Higgs oscillations [Collado et al. Phys. Rev. B 98, 214519 (2018)] can be observed as a transient effect. At long-times in contrast, dissipation leads to a steady state with a population imbalance that increases quadratically for small drives and saturates for large drives as in non-linear quantum optics. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant. We also compute the intensity of time- and angle-resolved photo-emission spectroscopy (tr-ARPES) and time-resolved tunneling spectra. The excited quasiparticle population appears as a decrease (increase) in the photo-emission intensity at energy $-\omega_d/2$ ($+\omega_d/2$) measured from the chemical potential. The tunneling intensity shows a time-dependent depression at $\pm\omega_d/2$ due to the lacking of spectral density and population unbalance causing Pauli blockade. We predict that at short times, compared to the energy relaxation time, both experiments will show oscillations with the Rabi-Higgs frequency.

Fate of dynamical phases of a BCS superconductor beyond the dissipationless regime

The BCS model of an isolated superconductor initially prepared in a nonequilibrium state, predicts the existence of interesting dynamical phenomena in the time-dependent order parameter as decaying oscillations, persistent oscillations and overdamped dynamics. To make contact with real systems remains an open challenge as one needs to introduce dissipation due to the environment in a self-consistent computation. Here, we reach this goal with the use of the Keldysh formalism to treat the effect of a thermal bath. We show that, contrary to the dissipationless case, all dynamical phases reach the equilibrium order parameter in a characteristic time that depends on the coupling with the bath. Remarkably, as time evolves, the overdamped phase shows a fast crossover where the superconducting order parameter recovers to reach a state with a well-developed long range order that tends towards equilibrium with the damped Higgs mode oscillations. Our results provide a benchmark for the description of the dynamics of real out-of-equilibrium superconductors relevant for quantum technological applications.

THE IMPACT OF BARYON PHYSICS ON THE STRUCTURE OF HIGH-REDSHIFT GALAXIES

We study the detailed structure of galaxies at redshifts z > 2 using cosmological simulations with improved modeling of the interstellar medium and star formation. The simulations follow the formation and dissociation of molecular hydrogen, and include star formation only in cold molecular gas. The molecular gas is more concentrated towards the center of galaxies than the atomic gas, and as a consequence, the resulting stellar distribution is very compact. For halos with total mass above 10^{11} Mo, the median half-mass radius of the stellar disks is 0.8 kpc at z = 3. The vertical structure of the molecular disk is much thinner than that of the atomic neutral gas. Relative to the non-radiative run, the inner regions of the dark matter halo change shape from prolate to mildly oblate and align with the stellar disk. However, we do not find evidence for a significant dark disk of dark matter around the stellar disk. The outer halo regions retain the orientation acquired during accretion and mergers, and are significantly misaligned with the inner regions. The radial profile of the dark matter halo contracts in response to baryon dissipation, establishing an approximately isothermal profile throughout most of the halo. This effect can be accurately described by a modified model of halo contraction. The angular momentum of a fixed amount of inner dark matter is approximately conserved over time, while in the dissipationless case most of it is transferred outward during mergers. The conservation of the dark matter angular momentum provides supporting evidence for the validity of the halo contraction model in a hierarchical galaxy formation process.

Geometric phase of neutrino propagating through dissipative matter

We study the geometric phase (GP) in neutrino oscillation for both Dirac and Majorana neutrinos. We apply the kinematic generalization of the GP to quantum open systems that take into account the coupling to a dissipative environment. In the dissipationless case, the GP does not depend on the Majorana angle. It is not the case in the presence of dissipation and hence the GP can serve as a tool determining the type of the Dirac vs the Majorana neutrino.

On the use of waveform images to describe the initial response of finite‐length waveguides

The d’Alembert solution of the wave equation can be adapted to describe reflection from planar boundaries. One technique for doing so images the incident wave on the opposite side of the boundary. This concept has been introduced in a few texts, most extensively by Morse and Ingard [Theoretical Acoustics, McGraw‐Hill, New York (1964), pp. 106–115], but only for nondissipative ends (infinite or zero impedance.) This paper formalizes the procedure for the case where the boundary has a resistive impedance that is independent of frequency, and then extends it to treat waveguides of finite length. It is shown that the field that results from arbitrary initial conditions can be represented by an infinite number of images. This leads to a representation of the acoustic field as oppositely propagating wave in an unbounded waveguide, with only a limited number of images overlapping at any instant. Both mathematical and graphical descriptions of these waves are derived. In addition to assisting the student to understand the evolution of the field, mathematical analysis of the image construction leads to a number of physical and mathematical insights to fundamental acoustic phenomena. These include the fact that the field in the dissipationless case can be represented as a modal series with associated natural frequencies, and a quantitative understanding of the manner in which the field decays when either end is dissipative. A corollary of the latter analysis is an expression for reverberation time that is remarkably similar to the Norris–Eyring formula. From an instructional viewpoint, the fact that all results are derived without recourse to solving differential equations makes the image waveform concept especially useful as a way of introducing new students to fundamental acoustic phenomena.

Analytic model for a weakly dissipative shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell-Segur (AKNS) scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.

Lossy effects in a nonlinear nematic optical fiber

We use the multiple scales method to derive a generalized nonlinear Schrödinger equation that takes into account the dissipative effects in the reorientation of a nematic confined in a cylindrical waveguide. This equation has soliton-like solutions and predicts a decrease in the penetration length of the optical solitons for each propagating mode with respect to the dissipationless case.

Single-particle treatment of quantum stochastic resonance

We first consider a test particle subjected to the simultaneous influence of a double-well mean field, thermal velocity distribution, external white noise and sinusoidal modulation. Within a path-integral framework the resulting power spectrum along with the signal-to-noise ratio (SNR) are expressed perturbatively in terms of the unperturbed eigenfunctions ψ n and eigenvalues E n , permitting us to demonstrate the existence of the phenomenon of quantum stochastic resonance (SR) in the dissipationless case. Next, we show that with the help of suitable transformations (viz., a complex Fourier frequency or a scaled-up potential) systems with weak friction or strong damping can be approximately mapped onto the dissipationless case. This yields a convenient method for studying frictional SR because the ψ n 's and E n 's can still be generated through a short-time propagator. Our formulation is illustrated numerically by displaying the variation of the SNR with the external noise strength and comparing the results vis-á-vis those obtained from classical stochastic simulation and quantum bath models. The usefulness of the single-particle approach to analyze the quantum SR phenomenon is emphasized.

Nonlinear instability and chaos in plasma wave–wave interactions. I. Introduction

Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave–wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.

Clump lifetime of relative motion in a stochastic force field

A Fokker-Plank equation describing the relative motion of two particles in a dissipative spacetime correlated turbulent force-field flow is derived, and the clump lifetime of the correlated motion for two adjacent particles with a small initial separation is found and compared with Dupree's results (1972) for the dissipationless case.

Formation of elliptical galaxies and massive halos

view Abstract Citations (35) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Formation of Elliptical Galaxies and Massive Halos Carlberg, R. G. ; Lake, G. ; Norman, C. A. Abstract In the present N-body models for the formation of spheroids of galaxies, the material starts in uniform expansion. For the dissipationless case, turnaround and collapse accompanied by the formation and destruction of substructure yields a smooth object, similar to an elliptical galaxy, whose core density is low and outer density gradient too steep. Dissipation is added with a simple scheme of 'sticky' particle collisions between neighboring gas clouds that turns them into collisionless 'stars' after a given specific number of collisions, yielding final densities that are closer to the r to the 1/4-power function. These experiments are extended to include a dissipationless and massive dark halo whose mass is 10 times greater than that of the gas. In the most extreme case of dissipation, the dark halo stars have isotropic velocity dispersions. Publication: The Astrophysical Journal Pub Date: January 1986 DOI: 10.1086/184591 Bibcode: 1986ApJ...300L...1C Keywords: Elliptical Galaxies; Galactic Evolution; Galactic Structure; Halos; Mass Distribution; Astronomical Models; Density Distribution; Galactic Nuclei; Many Body Problem; Star Distribution; Astrophysics; GALAXIES: FORMATION; GALAXIES: STRUCTURE full text sources ADS |

Quantum diffusion in dissipative systems.

The motion of a quantum-mechanical particle driven by a random fluctuating force is studied. Dissipation is introduced by coupling the particle to a continuous distribution of harmonic oscillators. A general expression for the mean-square displacement 〈${x}^{2}$(t)〉 is derived. It is shown that for long times t, one gets a crossover from a nondiffusive behavior 〈${x}^{2}$(t)〉\ensuremath{\propto}${t}^{3}$ for the dissipationless case to a diffusive one 〈${x}^{2}$(t)〉\ensuremath{\propto}t when dissipation is introduced. The case where the random driving force vanishes is also examined. Here the long-time behavior depends on the initial conditions of the oscillators and one gets 〈${x}^{2}$(t)〉\ensuremath{\propto}lnt if they are initially in their ground state (i.e., at zero temperature) and 〈${x}^{2}$(t)〉\ensuremath{\propto}Tt if they are initially at a finite temperature T.

Effect of viscosity on collective zener tunneling in charge density wave systems

The theory of Caldeira and Leggett on tunneling in the presence of viscous dissipation is extended and applied to the problem of collective Zener tunneling in quasi onedimensional charge density wave systems recently proposed by Bardeen. A finite bounce time is introduced and used as a variational parameter. Zener tunneling is given a real space formulation. The effective electric field dependent viscosity of the electrons is evaluated within the concept of the weakly pinned phase condensate. It is found that a strong coupling limit is realized where the coupling constant α is the ratio of Froehlich mass to band mass. The distance over which the electric field is effective in accelerating the Fermi sea is found to decrease by a factor of (2α)1/2 compared to the dissipationless case. This implies a corresponding increase in the activation field strengthE 0 in Zener's expressionP=exp(−E 0/E) for the tunneling probability. The new length appearing in the tunneling exponent seems to agree with the phase coherence length of a charge density wave pinned by weak impurities. Comparison to Maki's mechanism for depinning the charge density wave by solition pair creation is also made.

On the Theory of the Propagation of Plane, Finite Amplitude Waves in a Dissipative Fluid

The dissipationless theory for harmonic generation in an initially sinusoidal, plane, finite-amplitude wave is used as a basis for calculation of the harmonic components of such a wave in a fluid with dissipation. The assumption used is shown to lead approximately to the relationships of the Fox and Wallace theory. The result is given as a Fourier series, with graphs of the first few harmonic components for two specific cases. The series representation is valid for distances X⩽L, where L is the discontinuity distance for the dissipationless case.

A Fractional Termination for Ladder Networks

When using a uniform ladder network to simulate a smooth transmission line, the possibility is considered of deriving a termination which would be intermediate between the usual mid-shunt and mid-series types and which would have advantages over the latter. It is found that a new termination is possible which gives some improvement throughout a limited frequency range. For the dissipationless case, the range corresponds to a line of less than a quarter wave length. The improvements attainable are of the order of a few per cent and become less significant the greater the number of network sections. Thus, although the formula for the new termination and the estimates of the results which it will accomplish are given for any number of sections, the new termination is of most practical value for circuits of few sections. In arriving at this termination, consideration is given to the variation of each of the elements of the pair on each end; but of these two, the end element is the only one whose variation yields an improvement. For the frequency range for which the modified circuit is an improvement, the distinction between the two original types of termination largely is lost, the modified midshunt and modified mid-series terminations being almost identical. Beyond this range there is a difference between them, and the corresponding original and new networks are nearly equivalent. A possible application of the results is suggested in which the simulation of a smooth line is not involved.

A fractional termination for ladder networks

When using a uniform ladder network to simulate a smooth transmission line, the possibility is considered of deriving a termination which would be intermediate between the usual mid-shunt and mid-series types and which would have advantages over the latter. It is found that a new termination is possible which gives some improvement throughout a limited frequency range. For the dissipationless case, the range corresponds to a line of less than a quarter wave length. The improvements attainable are of the order of a few per cent and become less significant the greater the number of network sections. Thus, although the formula for the new termination and the estimates of the results which it will accomplish are given for any number of sections, the new termination is of most practical value for circuits of few sections. In arriving at this termination, consideration is given to the variation of each of the elements of the pair on each end; but of these two, the end element is the only one whose variation yields an improvement. For the frequency range for which the modified circuit is an improvement, the distinction between the two original types of termination largely is lost, the modified midshunt and modified mid-series terminations being almost identical. Beyond this range there is a difference between them, and the corresponding original and new networks are nearly equivalent. A possible application of the results is suggested in which the simulation of a smooth line is not involved.