scholarly journals Normal modes and time evolution of a holographic superconductor after a quantum quench

2014 ◽  
Vol 2014 (6) ◽  
Author(s):  
Xin Gao ◽  
Antonio M. García-García ◽  
Hua Bi Zeng ◽  
Hai-Qing Zhang
Keyword(s):  
Time Evolution ◽  
Normal Modes ◽  
Holographic Superconductor ◽  
Quantum Quench

Vibrational dynamics of polyatomic molecules in solution: assignment, time evolution and mixing of instantaneous normal modes

2010 ◽  
Vol 128 (4-6) ◽  
pp. 769-782 ◽  
Author(s):  
Adrián Kalstein ◽  
Sebastián Fernández-Alberti ◽  
Adolfo Bastida ◽  
Miguel Angel Soler ◽  
Marwa H. Farag ◽  
...  
Keyword(s):  
Time Evolution ◽  
Normal Modes ◽  
Polyatomic Molecules ◽  
Vibrational Dynamics ◽  
Instantaneous Normal Modes

Longitudinal sound waves in a collisionless, quasineutral plasma

2017 ◽  
Vol 83 (6) ◽  
Author(s):  
J. J. Ramos
Keyword(s):  
Electric Field ◽  
Time Evolution ◽  
Initial Conditions ◽  
Normal Modes ◽  
Adjoint Problem ◽  
Plasma Phys ◽  
Landau Damping ◽  
Linear Perturbation ◽  
Sound Waves ◽  
Quasineutral Plasma

The time evolution of slow sound waves in a homogeneous, collisionless and quasineutral plasma, in particular their Landau damping, is investigated using the kinetic-magnetohydrodynamics formulation of Ramos (J. Plasma Phys. vol. 81, 2015 p. 905810325; vol. 82, 2016 p. 905820607). In this approach, the electric field is eliminated from a closed, hybrid fluid-kinetic system that ensures automatically the fulfilment of the charge neutrality condition. Considering the time dependence of a spatial-Fourier-mode linear perturbation with wavevector parallel to the equilibrium magnetic field, this can be cast as a second-order self-adjoint problem with a continuum spectrum of real and positive squared frequencies. Therefore, a conventional resolution of the identity with a continuum basis of singular normal modes is guaranteed, which simplifies significantly a Van Kampen-like treatment of the Landau damping. The explicit form of such singular normal modes is obtained, along with their orthogonality relations. These are used to derive the damped time evolution of the fluid moments of solutions of initial-value problems, for the most general kinds of initial conditions. The non-zero parallel electric field is not used explicitly in this analysis, but it is calculated from any given solution after the later has been obtained.

scholarly journals Conditional nonlinear optimal perturbations of the double-gyre ocean circulation

2008 ◽  
Vol 15 (5) ◽  
pp. 727-734 ◽  
Author(s):  
A. D. Terwisscha van Scheltinga ◽  
H. A. Dijkstra
Keyword(s):  
Time Evolution ◽  
Ocean Circulation ◽  
Initial Perturbation ◽  
Normal Modes ◽  
Finite Amplitude ◽  
Dissipation Function ◽  
Stable States ◽  
Optimal Perturbation ◽  
Rectangular Basin ◽  
Double Gyre

Abstract. In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation threshold δ. Under symmetric wind forcing, a perfect pitchfork perturbation occurs in the model. The CNOPs are determined for all linearly stable states and the time evolution of the CNOPs is studied. It is found that the patterns of the CNOPs are similar to those of the non-normal modes for small te and approach those of the normal modes for larger te. With slightly asymmetric winds, an imperfect pitchfork occurs in the model. Indications are found that the time evolution of the CNOPs is related to the value of the dissipation function of the underlying steady state.

scholarly journals Time evolution of correlations in strongly interacting fermions after a quantum quench

2009 ◽  
Vol 79 (15) ◽  
Author(s):  
Salvatore R. Manmana ◽  
Stefan Wessel ◽  
Reinhard M. Noack ◽  
Alejandro Muramatsu
Keyword(s):  
Time Evolution ◽  
Strongly Interacting ◽  
Quantum Quench

scholarly journals Dissipative time evolution of a chiral state after a quantum quench

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
Stefan Wolff ◽  
Ameneh Sheikhan ◽  
Corinna Kollath
Keyword(s):  
Time Evolution ◽  
Quantum Quench

scholarly journals Perturbations and stability of rotating stars. I. Completeness of normal modes

1979 ◽  
Vol 368 (1734) ◽  
pp. 389-410 ◽  
Keyword(s):  
Initial Data ◽  
Eigenvalue Problem ◽  
Time Evolution ◽  
Normal Modes ◽  
Inner Product ◽  
Parallel Projection ◽  
Projection Operators ◽  
Quadratic Eigenvalue Problem ◽  
Linear Superposition ◽  
Quadratic Eigenvalue

Linear adiabatic perturbations of a differentially rotating, axisymmetric, perfect-fluid stellar model have normal modes described by a quadratic eigenvalue problem of the form where A and C are symmetric operators, B antisymmetric, and £ the Lagrangian displacement vector. We study this problem and the associated time evolution equation. We show that, in the Hilbert space H', whose norm is square-integration weighted by A, the operators A~lB and A~XC are anti-selfadjoint and selfadjoint, respectively, when restricted to vectors £ belonging to a particular but arbitrary axial harmonic. We then find bounds on the spectrum of normal modes and show that any initial data in the domain of C leads to a solution whose growth rate is limited by the spectrum and which can be expressed in a certain weak sense as a linear superposition of the normal modes. The normal modes are defined more precisely in terms of parallel projection operators associated with each isolated part of the spectrum. The quadratic eigenvalue problem can be reformulated in the space H' © ' (initial data space, or phase space) as a linear eigenvalue problem for an operator T, the generator of time evolution. This operator is not selfadjoint in H' © H' but it is selfadjoint in a Krein space (an indefinite inner-product space) formed by equipping H' © H' with the symplectic inner product. The normal modes are its eigenvectors and generalized eigenvectors.

scholarly journals Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Etienne Granet ◽  
Fabian Essler
Keyword(s):  
Time Evolution ◽  
Strong Coupling ◽  
Ground State ◽  
Strong Coupling Expansion ◽  
Full Time ◽  
Energy Eigenstates ◽  
Equilibrium Dynamics ◽  
Quantum Quench ◽  
Local Observables

We consider the time evolution of local observables after an interaction quench in the repulsive Lieb-Liniger model. The system is initialized in the ground state for vanishing interaction and then time-evolved with the Lieb-Liniger Hamiltonian for large, finite interacting strength c. We employ the Quench Action approach to express the full time evolution of local observables in terms of sums over energy eigenstates and then derive the leading terms of a 1/c expansion for several one and two-point functions as a function of time t>0 after the quantum quench. We observe delicate cancellations of contributions to the spectral sums that depend on the details of the choice of representative state in the Quench Action approach and our final results are independent of this choice. Our results provide a highly non-trivial confirmation of the typicality assumptions underlying the Quench Action approach.

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