Generalized conformal Hamiltonian dynamics and the pattern formation equations

Guha, Partha; Ghose‐Choudhury, A.

doi:10.1016/j.geomphys.2018.07.019

Cited by 11 publications

(9 citation statements)

References 21 publications

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“…The dynamics of the autocatalytic Gierer-Meinhardt system [40] can be obtained via conformal as well as contact Hamiltonian dynamics [9,41].…”

Section: Gierer-meinhardt Systemmentioning

confidence: 99%

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Generalized virial theorem for contact Hamiltonian systems

Ghosh¹

2023

Preprint

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We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling in a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The 'contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework.

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“…The dynamics of the autocatalytic Gierer-Meinhardt system [40] can be obtained via conformal as well as contact Hamiltonian dynamics [9,41].…”

Section: Gierer-meinhardt Systemmentioning

confidence: 99%

“…The dynamics of the Gierer-Meinhardt system can be equivalently described using contact Hamiltonian dynamics (see also [41]) if we consider an extended phase space M c = T * ℜ × ℜ ≅ ℜ 3 with a contact form η = dz − ydx.…”

Section: Gierer-meinhardt Systemmentioning

confidence: 99%

Generalized virial theorem for contact Hamiltonian systems

Ghosh¹

2023

Preprint

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“…In this section, we consider a particular class of dissipative quantum systems, which are those that admit a contact Hamiltonian description (see also [7,11,12,21,26,[36][37][38][39] for detailed discussions on the strengths and limitations of this approach both in the classical and quantum settings).…”

Section: Contact Geometry and Dynamics Of Dissipative N-level Quantum Systemsmentioning

confidence: 99%

From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics

2021

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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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“…This is the conformal Hamiltonian dynamics as described in [45]. See also [23]. Consider the vector field X generating the dynamics (3.20) and observe that, if the canonical symplectic twoform Ω = dq i ∧ dp i ,…”

Section: Canonical Hamiltonian Dynamics With Double Bracket Dissipationmentioning

confidence: 99%

On Geometrical Couplings of Dissipation and Curl Forces

Esen,

Guha,

Gümral

2021

Preprint

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Generalized conformal Hamiltonian dynamics and the pattern formation equations

Cited by 11 publications

References 21 publications

Generalized virial theorem for contact Hamiltonian systems

Generalized virial theorem for contact Hamiltonian systems

From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics

On Geometrical Couplings of Dissipation and Curl Forces

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