scholarly journals $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Paolo Ceschin ◽  
Riccardo Conti ◽  
Roberto Tateo
Keyword(s):  
Recent Literature ◽  
Equations Of Motion ◽  
Soliton Solutions ◽  
Relativistic Limit ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Quartic Potential ◽  
Composite Field ◽  
Dependent Change ◽  
Alternative Type

Abstract The $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed classical Lagrangian of a 2D Lorentz invariant theory can be derived from the original one, perturbed only at first order by the bare $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ composite field, through a field-dependent change of coordinates. Considering, as an example, the nonlinear Schrödinger (NLS) model with generic potential, we apply this idea to non-relativistic models. The form of the deformed Lagrangian contains a square-root and is similar but different from that for relativistic bosons. We study the deformed bright, grey and Peregrine’s soliton solutions. Contrary to naive expectations, the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -perturbation of nonlinear Schrödinger NLS with quartic potential does not trivially emerge from a standard non-relativistic limit of the deformed sinh-Gordon field theory. The c → ∞ outcome corresponds to a different type of irrelevant deformation. We derive the corresponding Poisson bracket structure, the equations of motion and discuss various interesting aspects of this alternative type of perturbation, including links with the recent literature.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

Consistent section-averaged equations of quasi-one-dimensional laminar flow

2010 ◽  
Vol 656 ◽  
pp. 337-341 ◽  
Author(s):  
PAOLO LUCHINI ◽  
FRANÇOIS CHARRU
Keyword(s):  
Equations Of Motion ◽  
Stability Result ◽  
Momentum Equation ◽  
Dissipation Function ◽  
Dimensional Solution ◽  
First Order ◽  
Averaged Equations ◽  
Classical Stability ◽  
Momentum Integral ◽  
Free Falling

Section-averaged equations of motion, widely adopted for slowly varying flows in pipes, channels and thin films, are usually derived from the momentum integral on a heuristic basis, although this formulation is affected by known inconsistencies. We show that starting from the energy rather than the momentum equation makes it become consistent to first order in the slowness parameter, giving the same results that have been provided until today only by a much more laborious two-dimensional solution. The kinetic-energy equation correctly provides the pressure gradient because with a suitable normalization the first-order correction to the dissipation function is identically zero. The momentum equation then correctly provides the wall shear stress. As an example, the classical stability result for a free falling liquid film is recovered straightforwardly.

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