Related papers: Time-ordering and a generalized Magnus expansion
We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the…
The Magnus expansion provides an exponential representation of one-parameter operator families, expressed as a series expansion in its generators. This is useful for example in quantum mechanics for expressing a unitary evolution determined…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…
In 1932, Fermi presented a two-atom model for determining whether quantum mechanics is consistent with causality, and concluded that indeed it is. In the late 1960's, Shirokov and others found that Fermi's approximations may not have been…
Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is…
We investigate the Magnus expansion for a generic time-dependent two-level system under single-axis driving.By virtue of the su(2) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate the usefulness of the…
We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.
In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced…
In general-covariant theories the Hamiltonian is a constraint, and hence there is no time evolution; this is the problem of time. In the subcritical free string, the Hamiltonian ceases to be a constraint after quantization due to conformal…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
The time-marching strategy, which propagates the solution from one time step to the next, is a natural strategy for solving time-dependent differential equations on classical computers, as well as for solving the Hamiltonian simulation…
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…
We re-examine the notions of time and evolution in the light of the mathematical properties of the solutions of the Wheeler-DeWitt equation which are revealed by an extended adiabatic treatment. The main advantage of this treatment is to…
Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed time order while in general relativity temporal order is influenced by the distribution of matter. When…