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Journal articles on the topic 'Dissipative approach'

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Published: 10 March 2023

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1

CHRISTOV, C. I. "DISSIPATIVE QUASI-PARTICLES: THE GENERALIZED WAVE EQUATION APPROACH." International Journal of Bifurcation and Chaos 12, no. 11 (November 2002): 2435–44. http://dx.doi.org/10.1142/s0218127402005959.

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Generalized Wave Equations containing dispersion, dissipation and energy-production (GDWE) are considered in lieu of dissipative NEE as more suitable models for two-way interaction of localized waves. The quasi-particle behavior and the long-time evolution of localized solutions upon take-over and head-on collisions are investigated numerically by means of an adequate difference scheme which represents faithfully the balance/conservation laws. It is shown that in most cases the balance between energy production/dissipation and nonlinearity plays a similar role to the classical Boussinesq balance between dispersion and nonlinearity, namely it can create and support localized solutions which behave as quasi-particles upon collisions and for a reasonably long time after that.

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2

Mayorga, M. "Upper Bound for the Entropy Production and Dissipative Particle Dynamics." International Journal of Modern Physics C 09, no. 08 (December 1998): 1299–306. http://dx.doi.org/10.1142/s0129183198001175.

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The upper bound for the entropy production of a dense gas is presented and its connection with the so-called Fisher information measure is revised. The relation with dissipative particle dynamics is analyzed, which serve to identify the thermostat for the fluid system. The analogy with a turbulence approach, a probabilistic approach to dynamical sytems, detailed balance for dissipative particle dynamics and fluctuation dissipation theorems for relaxing systems is presented.

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3

Bhattacharya, Samyadeb, and Sisir Roy. "Dissipative Effect and Tunneling Time." Advances in Mathematical Physics 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/138358.

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The quantum Langevin equation has been studied for dissipative system using the approach of Ford et al. Here, we have considered the inverted harmonic oscillator potential and calculated the effect of dissipation on tunneling time, group delay, and the self-interference term. A critical value of the friction coefficient has been determined for which the self-interference term vanishes. This approach sheds new light on understanding the ion transport at nanoscale.

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4

AURICCHIO, FERDINANDO, ELENA BONETTI, and ANTONIO MARIGONDA. "A METRIC APPROACH TO PLASTICITY VIA HAMILTON–JACOBI EQUATION." Mathematical Models and Methods in Applied Sciences 20, no. 09 (September 2010): 1617–47. http://dx.doi.org/10.1142/s0218202510004726.

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Thermodynamical consistency of plasticity models is usually written in terms of the so-called "maximum dissipation principle". In this paper, we discuss constitutive relations for dissipative materials written through suitable generalized gradients of a (possibly non-convex) metric. This new framework allows us to generalize the classical results providing an interpretation of the yield function in terms of Hamilton–Jacobi equations theory.

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5

LÓPEZ, G., M. MURGUÍA, and M. SOSA. "TIME-INDEPENDENT APPROACH FOR DISSIPATIVE SYSTEMS." Modern Physics Letters B 10, no. 24 (October 20, 1996): 1197–203. http://dx.doi.org/10.1142/s021798499600136x.

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A new dissipative model is proposed for the small component of a mixture of a small and large component of gases, where the large component is treated as an ideal gas. The thermodynamic characteristics of the gas are derived through a statistical mechanical approach. The model requires for the small component to have a big dimension and its number of particles to be smaller than the large one. Using the associated partition function, the internal energy and the equation of state are calculated. The internal energy does not suffer any deviation from that of the two component ideal gas, but the equation of state deviates from that of the ideal gas for large values of the parameter which characterizes the dissipative model.

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6

Sakagami, M. a., and T. Kubota. "Path Integral Approach to Dissipative Processes." Progress of Theoretical Physics 76, no. 2 (August 1, 1986): 548–60. http://dx.doi.org/10.1143/ptp.76.548.

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7

Bose, Thomas, and Steffen Trimper. "Lagrangian approach and dissipative magnetic systems." Physics Letters A 375, no. 24 (June 2011): 2452–55. http://dx.doi.org/10.1016/j.physleta.2011.05.019.

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8

Ankiewicz, Adrian, Nail Akhmediev, and Natasha Devine. "Dissipative solitons with a Lagrangian approach." Optical Fiber Technology 13, no. 2 (April 2007): 91–97. http://dx.doi.org/10.1016/j.yofte.2006.12.001.

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9

ABE, Y., C. GRÉGOIRE, and H. DELAGRANGE. "LANGEVIN APPROACH TO NUCLEAR DISSIPATIVE DYNAMICS." Le Journal de Physique Colloques 47, no. C4 (August 1986): C4–329—C4–338. http://dx.doi.org/10.1051/jphyscol:1986436.

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10

Civelek, Cem. "Observability, controllability and stability of a nonlinear RLC circuit in form of a Duffing oscillator by means of theoretical mechanical approach." Journal of Electrical Engineering 73, no. 2 (April 1, 2022): 140–45. http://dx.doi.org/10.2478/jee-2022-0018.

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Abstract In this research article, observability, controllability and stability of a nonlinear RLC circuit with a nonlinear capacitor is investigated as a Duffing oscillator beginning with the dissipative equations of generalized motion using Lagrange-dissipative model ({L, D} -model briefly). The force related to the potential energy, equilibria, and their well known stability properties are given using state space approach. Prerequisite that the condition for a Legendre transform is fulfilled, for the same system, also Hamiltonian of the system is found. Using Hamiltonian and dissipation function, dissipative canonical equations are obtained. These equations are written in state space form. Then the equality to the same results obtained using the dissipative equations of generalized motion related equilibria and their stability was shown. Thus a Lyapunov function as residual energy function (REF) is justified in terms of stability of the overall system. As last step, different electrical and mechanical (physical) realization possibilities are discussed.

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11

Zhang, Jian Wei, Hai Jun Chen, Sheng Jun Wang, and Yuan Ren. "Variational Solution of Steady-Structure in Exciton-Polariton Condensates with a Modified Lagrangian Approach." Key Engineering Materials 787 (November 2018): 113–22. http://dx.doi.org/10.4028/www.scientific.net/kem.787.113.

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Exciton-polariton condensate is a new kind of system exhibiting spontaneous coherence, which is a new quantum dissipation system. Numerical simulation and analytical methods can be used to study the static and dynamical properties of exciton-polariton condensate. In this paper, A modified Lagrangian method is developed for exciton-polariton system to find the steady-state structure and regimes among the parameters of the system, and two new forms of trial wave function are proposed. The modified Lagrangian method is successfully applied to the exciton-polariton system described by the open-dissipative Gross-Pitaevskii equation for the first time. Furthermore, static version of the modified Lagrangian method provides stationary shape of the steady-state structure, while the time-dependent version can be used to study small amplitude oscillations around stationary states. On the one hand, comparison of the profiles for steady-state structure, predicted by the modified Lagrangian and those found from numerical solution of the open-dissipative Gross-Pitaevskii(dGP) equation shows good agreement, thereby proving the accuracy of the trial wave function and validating the proposed approach. Particularly, this new method promotes the deeper cognition and understanding for the dissipative exciton-polariton system and is helpful to explore the mechanism of the gain and dissipation effect on the steady-state structure of the system.

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12

Feldmeier, H. "Transport phenomena in dissipative heavy-ion collisions: the one-body dissipation approach." Reports on Progress in Physics 50, no. 8 (August 1, 1987): 915–94. http://dx.doi.org/10.1088/0034-4885/50/8/001.

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13

Mar’yan, M. I., and N. V. Yurkovych. "Dissipative Structures and Fractal Approach to the Formation of Non-Crystalline States." Фізика і хімія твердого тіла 17, no. 1 (March 15, 2016): 31–36. http://dx.doi.org/10.15330/pcss.17.1.31-36.

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Found that the formation of fractal dissipative structures in non-crystalline solids associated with the creation of self-consistent fields of soft atomic configurations and thermal behavior of such structure-sensitive characteristics that meet the minimum energy dissipation for a given external parameters - speed cooling and process modes receipt. It is shown that this fact makes it possible to determine the non-crystalline structure through the processes of self-organization.

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14

Brannick, J., C. Liu, T. Qian, and H. Sun. "Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach." Numerical Mathematics: Theory, Methods and Applications 8, no. 2 (May 2015): 220–36. http://dx.doi.org/10.4208/nmtma.2015.w12si.

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AbstractIn this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.

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15

Kim, Wooram, and J. N. Reddy. "An Improved Time Integration Algorithm: A Collocation Time Finite Element Approach." International Journal of Structural Stability and Dynamics 17, no. 02 (March 2017): 1750024. http://dx.doi.org/10.1142/s0219455417500249.

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A time collocation finite element approach is employed to develop one- and two-step time integration schemes with algorithmic dissipation control capability. The newly developed time integration schemes are combined to obtain a new family of time integration algorithms using the concept employed by Baig and Bathe. The newly developed algorithm can effectively control the algorithmic dissipation by relating the collocation parameters with the spectral radius in the high frequency limit. The new algorithm provides better accuracy compared with the generalized-[Formula: see text] method for highly dissipative cases and includes the Baig and Bathe method within its family as a special case.

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16

Ferreira, M. F., and S. C. Latas. "A Variational Approach to Dissipative Optical Solitons." Journal of Physics: Conference Series 1730, no. 1 (January 1, 2021): 012019. http://dx.doi.org/10.1088/1742-6596/1730/1/012019.

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17

El-Nabulsi, R. A. "Fractional Variational Approach for Dissipative Mechanical Systems." Analysis in Theory and Applications 30, no. 3 (June 2014): 249–59. http://dx.doi.org/10.4208/ata.2014.v30.n3.1.

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18

ULGEN, Ibrahim, and Bulent YILMAZ. "Dissipative dynamics within stochastic mean-field approach." Bitlis Eren University Journal of Science and Technology 9, no. 2 (December 27, 2019): 104–8. http://dx.doi.org/10.17678/beuscitech.633558.

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19

Belur, Madhu N., Harish K. Pillai, and H. L. Trentelman. "Dissipative systems synthesis: A linear algebraic approach." Linear Algebra and its Applications 425, no. 2-3 (September 2007): 739–56. http://dx.doi.org/10.1016/j.laa.2007.04.016.

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20

Lowe, C. P. "An alternative approach to dissipative particle dynamics." Europhysics Letters (EPL) 47, no. 2 (July 15, 1999): 145–51. http://dx.doi.org/10.1209/epl/i1999-00365-x.

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21

Adorno, A., A. Bonasera, M. Di Toro, C. Gregoire, and F. Gulminelli. "Dissipative fragmentation in a phase space approach." Nuclear Physics A 488 (October 1988): 451–56. http://dx.doi.org/10.1016/0375-9474(88)90281-3.

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22

Ford, G. W., J. T. Lewis, and R. F. O'Connell. "Dissipative quantum tunneling: quantum Langevin equation approach." Physics Letters A 128, no. 1-2 (March 1988): 29–34. http://dx.doi.org/10.1016/0375-9601(88)91037-7.

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23

Chen, Xiaowei, Mingzhan Song, and Songhe Song. "A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model." Mathematics 8, no. 8 (July 28, 2020): 1238. http://dx.doi.org/10.3390/math8081238.

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We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.

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24

Xie, Yun, Zhuangyu Liu, Xiaoli Luan, and Jiwei Wen. "Dissipative dynamic output feedback control for switched systems via multistep Lyapunov function approach." Transactions of the Institute of Measurement and Control 41, no. 15 (June 17, 2019): 4254–62. http://dx.doi.org/10.1177/0142331219854867.

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The conservatism reduction problem of dissipative dynamic output feedback (DOF) control for a class of average dwell time switched system is investigated via a multistep Lyapunov function (LF) approach. First, a larger dissipative region with guaranteed stability and specifically, smaller [Formula: see text] level can be achieved by increasing a predictive step N, which means the monotonic requirement of LF is relaxed. Then, based on the results of dissipative analysis, a robust dissipative DOF controller is further designed. Unlike the traditional method that introduces equality constraint to obtain numerical testable conditions with heuristic nature, a less conservative controller is designed, where the LF matrix is formulated without structural constraint.

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25

Pavlov G. A. "Fluctuation-dissipation theorem and frequency moments of response functions of a dense plasma to an electromagnetic field." Technical Physics 92, no. 2 (2022): 191. http://dx.doi.org/10.21883/tp.2022.02.52945.149-21.

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The fluctuation-dissipative theorem and frequency moments for quadratic functions of the reaction of a dense plasma in a constant magnetic field to an electromagnetic field are considered. The frequency moments of the corresponding correlation functions are studied. A model approach is proposed to calculate quadratic reaction functions that determine nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) in a constant magnetic field. Keywords: dense plasma, nonlinear fluctuation-dissipative theorem, quadratic reaction functions, nonlinear phenomena. Keywords: dense plasma, nonlinear fluctuation-dissipation theorem, quadratic response functions, nonlinear phenomena.

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26

Öztürk, Fahri Emre, Tim Lappe, Göran Hellmann, Julian Schmitt, Jan Klaers, Frank Vewinger, Johann Kroha, and Martin Weitz. "Observation of a non-Hermitian phase transition in an optical quantum gas." Science 372, no. 6537 (April 1, 2021): 88–91. http://dx.doi.org/10.1126/science.abe9869.

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Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate’s second-order coherence. The phase transition occurs because of the emergence of an exceptional point in the quantum gas. Although Bose-Einstein condensation is usually connected to lasing by a smooth crossover, the observed phase transition separates the biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our approach can be used to study a wide class of dissipative quantum phases in topological or lattice systems.

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27

Kalashnikov, V. L., and S. Wabnitz. "Stabilization of spatiotemporal dissipative solitons in multimode fiber lasers by external phase modulation." Laser Physics Letters 19, no. 10 (August 11, 2022): 105101. http://dx.doi.org/10.1088/1612-202x/ac8678.

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Abstract In this work, we introduce a method for the stabilization of spatiotemporal (ST) solitons. These solitons correspond to light bullets in multimode optical fiber lasers, energy-scalable waveguide oscillators and amplifiers, localized coherent patterns in Bose–Einstein condensates, etc. We show that a three-dimensional confinement potential, formed by a spatial transverse (radial) parabolic graded refractive index and dissipation profile, in combination with quadratic temporal phase modulation, may permit the generation of stable ST dissipative solitons. This corresponds to combining phase mode-locking with the distributed Kerr-lens mode-locking. Our study of the soliton characteristics and stability is based on analytical and numerical solutions of the generalized dissipative Gross–Pitaevskii equation. This approach could lead to higher energy (or condensate mass) harvesting in coherent spatio-temporal beam structures formed in multimode fiber lasers, waveguide oscillators, and weakly-dissipative Bose–Einstein condensates.

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28

Moreno, Jaime A. "Observer design for bioprocesses using a dissipative approach." IFAC Proceedings Volumes 41, no. 2 (2008): 15559–64. http://dx.doi.org/10.3182/20080706-5-kr-1001.02631.

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29

Nguyen, Sonnet Q. H., and Łukasz A. Turski. "On the Dirac approach to constrained dissipative dynamics." Journal of Physics A: Mathematical and General 34, no. 43 (October 19, 2001): 9281–302. http://dx.doi.org/10.1088/0305-4470/34/43/312.

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30

Misawa, Tetsuya. "Stochastic variational approach to quantal-dissipative dynamical systems." Physical Review A 40, no. 6 (September 1, 1989): 3387–96. http://dx.doi.org/10.1103/physreva.40.3387.

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31

Smith, C. Morais, and A. O. Caldeira. "Generalized Feynman-Vernon approach to dissipative quantum systems." Physical Review A 36, no. 7 (October 1, 1987): 3509–11. http://dx.doi.org/10.1103/physreva.36.3509.

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32

Muñoz-Lecanda, Miguel C., and F. Javier Yániz-Fernández. "Dissipative Control of Mechanical Systems: A Geometric Approach." SIAM Journal on Control and Optimization 40, no. 5 (January 2002): 1505–16. http://dx.doi.org/10.1137/s0363012900374804.

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33

Moreno, Jaime A. "Observer Design for Nonlinear Systems: A Dissipative Approach." IFAC Proceedings Volumes 37, no. 21 (December 2004): 681–86. http://dx.doi.org/10.1016/s1474-6670(17)30549-9.

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34

Pavel, L., and F. W. Fairman. "Nonlinear H/sub ∞/ control: a J-dissipative approach." IEEE Transactions on Automatic Control 42, no. 12 (1997): 1636–53. http://dx.doi.org/10.1109/9.650014.

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35

Niita, K., W. N�renberg, and S. J. Wang. "Selfconsistent diabatic approach to dissipative collective nuclear motion." Zeitschrift f�r Physik A Atomic Nuclei 326, no. 1 (March 1987): 69–77. http://dx.doi.org/10.1007/bf01294573.

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36

Chávez Cerda, S., S. B. Cavalcanti, and J. M. Hickmann. "A variational approach of nonlinear dissipative pulse propagation." European Physical Journal D - Atomic, Molecular and Optical Physics 1, no. 3 (April 1, 1998): 313–16. http://dx.doi.org/10.1007/s100530050098.

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37

Niita, K., W. N�renberg, and S. J. Wang. "Selfconsistent diabatic approach to dissipative collective nuclear motion." Zeitschrift f�r Physik A Atomic Nuclei 328, no. 4 (December 1987): 503. http://dx.doi.org/10.1007/bf01289641.

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38

Macintosh, Robert, and Donald Maclean. "Conditioned emergence: a dissipative structures approach to transformation." Strategic Management Journal 20, no. 4 (April 1999): 297–316. http://dx.doi.org/10.1002/(sici)1097-0266(199904)20:4<297::aid-smj25>3.0.co;2-q.

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39

Chen, Yu. "Dissipative linear response theory and its appications in open quantum systems." Acta Physica Sinica 70, no. 23 (2021): 230306. http://dx.doi.org/10.7498/aps.70.20211687.

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With the recent development of experimental technology, the ability to control the dissipation in quantum many-body system is greatly enhanced. Meanwhile, many new breakthroughs are achieved in detecting the quantum states and others. All these advances make it necessary to establish a new theory for calculating the dissipative dynamics in strongly correlated sstems. Very recently, we found that by taking the interactions between the system and the bath as a perturbation, a systematic dissipative response theory can be established. In this new approach, the calculation of dissipative dynamics for any physical observables and the entropies can be converted into the calculation of certain correlation functions in initial states. Then we discuss how Markovian approximation at low temperature limit and at high temperature limit can be reached Also, we review the progress of the dissipative dynamics in open Bose-Hubbard model. In the fourth section, we review recent progress of entropy dynamics of quench dynamics of an open quantum system. Finally, we draw a conclusion and discuss possible development in the future.

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40

Civelek, Cem. "Analysis of a coupled physical discrete time system by means of extended Euler-Lagrange difference equation and discrete dissipative canonical equation." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 6 (October 24, 2019): 1810–27. http://dx.doi.org/10.1108/compel-04-2019-0163.

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Purpose The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete. Design/methodology/approach The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well. Findings Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented. Originality/value The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

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41

Mamaev, M., L. C. G. Govia, and A. A. Clerk. "Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer." Quantum 2 (March 27, 2018): 58. http://dx.doi.org/10.22331/q-2018-03-27-58.

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We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED.

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42

CARTER, BRANDON, and NICOLAS CHAMEL. "COVARIANT ANALYSIS OF NEWTONIAN MULTI-FLUID MODELS FOR NEUTRON STARS III: TRANSVECTIVE, VISCOUS, AND SUPERFLUID DRAG DISSIPATION." International Journal of Modern Physics D 14, no. 05 (May 2005): 749–74. http://dx.doi.org/10.1142/s0218271805006845.

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As a follow up to papers dealing firstly with a convective variational formulation in a Milne–Cartan framework for non-dissipative multi-fluid models, and secondly with various ensuing stress energy conservation laws and generalized virial theorems, this work continues a series showing how analytical procedures developed in the context of General Relativity can be usefully adapted for implementation in a purely Newtonian framework where they provide physical insights that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. The present paper describes the 4-dimensionally covariant treatment of various dissipative mechanisms, including viscosity in non-superfluid constituents, superfluid vortex drag, ordinary resistivity (mutual friction) between relatively moving non-superfluid constituents, and the transvective dissipation that occurs when matter is transformed from one constituent to another due to chemical disequilibrium such as may be produced by meridional circulation in neutron stars. The corresponding non-dissipative limit cases of vortex pinning, convection and chemical equilibrium are also considered.

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43

Bona, J. L., F. Demengel, and K. Promislow. "Fourier splitting and dissipation of nonlinear dispersive waves." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 3 (1999): 477–502. http://dx.doi.org/10.1017/s0308210500021478.

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Presented herein is a new method for analysing the long-time behaviour of solutions of nonlinear, dispersive, dissipative wave equations. The method is applied to the generalized Korteweg–de Vries equation posed on the entire real axis, with a homogeneous dissipative mechanism included. Solutions of such equations that commence with finite energy decay to zero as time becomes unboundedly large. In circumstances to be spelled out presently, we establish the existence of a universal asymptotic structure that governs the final stages of decay of solutions. The method entails a splitting of Fourier modes into long and short wavelengths which permits the exploitation of the Hamiltonian structure of the equation obtained by ignoring dissipation. We also develop a helpful enhancement of Schwartz's inequality. This approach applies particularly well to cases where the damping increases in strength sublinearly with wavenumber. Thus the present theory complements earlier work using centre-manifold and group-renormalization ideas to tackle the situation wherein the nonlinearity is quasilinear with regard to the dissipative mechanism.

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44

Zloshchastiev, Konstantin G. "Model Hamiltonians of open quantum optical systems: Evolvement from hermiticity to adjoint commutativity." Journal of Physics: Conference Series 2407, no. 1 (December 1, 2022): 012011. http://dx.doi.org/10.1088/1742-6596/2407/1/012011.

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Abstract In the conventional quantum mechanics of conserved systems, Hamiltonian is assumed to be a Hermitian operator. However, when it comes to quantum systems in presence of dissipation and/or noise, including open quantum optical systems, the strict hermiticity requirement is nor longer necessary. In fact, it can be substantially relaxed: the non-Hermitian part of a Hamiltonian is allowed, in order to account for effects of dissipative environment, whereas its Hermitian part would be describing subsystem’s energy. Within the framework of the standard approach to dissipative phenomena based on a master equation for the reduced density operator, we propose a replacement of the hermiticity condition by a more general condition of commutativity between Hermitian and anti-Hermitian parts of a Hamiltonian. As an example, we consider a dissipative two-mode quantum system coupled to a single-mode electromagnetic wave, where we demonstrate that the adjoint-commutativity condition does simplify the parametric space of the model.

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45

Chen, Xi, and Corina Drapaca. "On the dissipation of conforming and discontinuous Galerkin schemes for the incompressible Navier–Stokes equations." AIP Advances 12, no. 7 (July 1, 2022): 075004. http://dx.doi.org/10.1063/5.0080842.

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In this paper, we improve the numerical performance of the classical conforming finite element schemes for the time-dependent incompressible Navier–Stokes equations by adding dissipation. This is a physics-inspired approach, and the dissipative terms are constructed through the discontinuity of numerical quantities across interior edges and, therefore, decouple the space and time discretizations when compared with the streamline-upwind Petrov–Galerkin for the time-marching methods. In particular, the order of h (edge diameter) in the dissipative terms is motivated by the energy stability and error equation associated with the unsteady problem. Furthermore, we point out that the added dissipation may also be viewed as an alternative for the grad-div stabilization from the physical approach in the unsteady problem. The added dissipation is naturally within the framework of the variational multiscale and thus could serve as implicit subgrid-scale models in large eddy simulations. Numerical experiments with a jump of the gradient are performed. In addition, we test the ideas with the discontinuous Galerkin formulations. Numerical results indicate that our suggested dissipation is helpful in reducing numerical errors and is competitive when compared with other conventional stabilization available in the literature. Finally, we show that the changes in the physical role of the same terms may significantly change their corresponding numerical behaviors through examples on the steady problems.

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Ikeda, Tatsuhiko N., and Masahiro Sato. "General description for nonequilibrium steady states in periodically driven dissipative quantum systems." Science Advances 6, no. 27 (July 2020): eabb4019. http://dx.doi.org/10.1126/sciadv.abb4019.

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Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.

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Cruz-Prado, Hans, Alessandro Bravetti, and Angel Garcia-Chung. "From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics." Quantum Reports 3, no. 4 (October 12, 2021): 664–83. http://dx.doi.org/10.3390/quantum3040042.

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Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.

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Cruz-Prado, Hans, Alessandro Bravetti, and Angel Garcia-Chung. "From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics." Quantum Reports 3, no. 4 (October 12, 2021): 664–83. http://dx.doi.org/10.3390/quantum3040042.

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Abstract:

Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of the states is preserved. Our proposal consists of extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation by using appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems for which it is shown, by means of the corresponding contact master equation, that the resulting dynamics constitute a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.

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49

Yamamoto, Naoki. "Pure Gaussian state generation via dissipation: a quantum stochastic differential equation approach." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5324–37. http://dx.doi.org/10.1098/rsta.2011.0529.

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Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then, a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.

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Zhang, Jiangyi, Vicente Romero-García, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Dimitrios Frantzeskakis. "Dark Solitons in Acoustic Transmission Line Metamaterials." Applied Sciences 8, no. 7 (July 20, 2018): 1186. http://dx.doi.org/10.3390/app8071186.

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We study dark solitons, namely density dips with a phase jump across the density minimum, in a one-dimensional, weakly lossy nonlinear acoustic metamaterial, composed of a waveguide featuring a periodic array of side holes. Relying on the electroacoustic analogy and the transmission line approach, we derive a lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. The latter, using the method of multiple scales, is reduced to a defocusing nonlinear Schrödinger equation, which leads to dark soliton solutions. The dissipative dynamics of these structures is studied via soliton perturbation theory. We investigate the role—and interplay between—nonlinearity, dispersion and dissipation on the soliton formation and dynamics. Our analytical predictions are corroborated by direct numerical simulations.

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