Related papers: Analogue of Hamilton-Jacobi theory for the time-ev…
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
We prove a homogenization result for a family of time-dependent Hamilton-Jacobi equations, rescaled by a parameter $\varepsilon$ tending to zero, posed on a periodic network, with a suitable notion of periodicity that will be defined. As…
How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a…
In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be…
We can incorporate a "time" evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of states in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation.…
Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of…
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is…
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. We present a new and simple proof of the rate of convergence of the approximations based on the adjoint method recently…
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic…
We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock…
We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…
We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems.…
We present a quantum averaging theory (QAT) for analytically modeling unitary gate dynamics in driven quantum systems beyond the rotating-wave approximation. QAT addresses the simultaneous presence of distinct timescales by generating a…
We propose a `Floquet engineering' formalism to systematically design a periodic driving protocol in order to stroboscopically realize the desired system starting from a given static Hamiltonian. The formalism is applicable to quantum…
We study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and…