Maupertuis-Hamilton least action principle in the space of variational parameters for Schrödinger dynamics; A dual time-dependent variational principle
نویسندگان
چکیده
منابع مشابه
The Jacobi-Maupertuis Principle in Variational Integrators
In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V{q), the curve traced out by the system on a constant energy surface minimizes the action given by / y^2{E — V{q))ds where ds is the line element on the constant energy su...
متن کامل$(varphi_1, varphi_2)$-variational principle
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Ma...
متن کاملTime-dependent variational principle for quantum lattices.
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, a...
متن کاملThe Second Entropy: A Variational Principle for Time-dependent Systems
The fundamental optimization principle for non-equilibrium thermodynamics is given. The second entropy is introduced as the quantity that is maximised to determine the optimum state of a non-equilibrium system. In contrast, the principles of maximum or minimum dissipation, which have previously been proposed by Onsager, Prigogine, and others as the variational principle for such systems, are sh...
متن کاملA Variational Principle in Discrete Space-Time – Existence of Minimizers
We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations. In a recent book it was proposed to formulate physics with a new variational principle in space-time [2]. In the present paper we construct minimizers of this variational principle. In order to make the presentation self-contained...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics Communications
سال: 2020
ISSN: 2399-6528
DOI: 10.1088/2399-6528/ab7b34