Related papers: Adiabatic invariants drive rhythmic human motion i…
We show that the definition of instantaneous eigenstate populations for a dynamical non-self-adjoint system is not obvious. The naive direct extension of the definition used for the self-adjoint case leads to inconsistencies; the resulting…
We construct an extensive adiabatic invariant for a Klein-Gordon chain in the thermodynamic limit. In particular, given a fixed and sufficiently small value of the coupling constant $a$, the evolution of the adiabatic invariant is…
We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in…
Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first…
We investigate gauge invariance against phase space shifting in nonequilibrium systems, as represented by time-dependent many-body Hamiltonians that drive an initial ensemble out of thermal equilibrium. The theory gives rise to gauge…
We consider the adiabatic charge transport through zero-dimensional mesoscopic sample (quantum dot) caused by two periodically changing external perturbations. Both the magnitude and the sign of the transmitted charge are extremely…
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up…
One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation,…
Human movements are physical processes combining the classical mechanics of the human body moving in space and the biomechanics of the muscles generating the forces acting on the body under sophisticated sensory-motor control. One way to…
We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes adiabatically its sign. We show that after a single magnetic field passage through zero…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
The biomechanics of the human body gives subjects a high degree of freedom in how they can execute movement. Nevertheless, subjects exhibit regularity in their movement patterns. One way to account for this regularity is to suppose that…
In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude of a strongly localized mode (a trapped wave) can be…
The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the…
We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action…
The problem of biped locomotion at steady speeds is discussed through a Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant…
Dynamic motions of humans and robots are widely driven by posture-dependent nonlinear interactions between their degrees of freedom. However, these dynamical effects remain mostly overlooked when studying the mechanisms of human movement…
For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled…