Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

We show that a laser pulse can always be found that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are computed to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). As a result, the observed induced dipolar spectra without detailed information on the driving field is not sufficient to characterize atomic and molecular systems. The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flexibilities of nonlinear optics.PACS numbers: 03.65. Pm, 05.60.Gg, 05.20.Dd, 52.65.Ff, 03.50.Kk Introduction. One system imitating another different system, known as mimicry, abounds in the sciences. For example, in biology [1][2][3], different species often change their appearance in order to hide from predators. In material science [4][5][6][7] and chemistry [8][9][10][11][12], simpler and cheaper compounds one sought to mimic the properties of more complex and expensive materials. In this Letter, we introduce the method of Spectral Dynamic Mimicry (SDM) bringing imitation into the domain of optics via quantum control. Thereby, SDM may be viewed as realizing an aspect of the alchemist dream to make different elements or materials look alike, albeit for the duration of a control laser pulse.Summary of results. We want the induced dipole spectra (IDS) of an N -electron system, y(t) = N k=1 x k , to follow (i.e., track) a predefined time-dependent vector Y (t); atomic units (a.u.) with = m = e = 1 are used throughout. In particular, assuming that y(t) = Y (t) at some time moment t, then the control field E(t + dt) enforcing y(t + dt) = Y (t + dt) at the next time step t + dt is given bywhere dt is an infinitesimal time increment, −∇ k V ( x k ) (t) and A k (t) describe the interaction with a potential force and an environment, respectively (see Sec. I of Supplemental Material [13] for details, which includes Ref. [14]). The state (i.e., the density matrix and the probability distribution in the quantum and classical cases, respectively) determining the expectation values is propagated to the next time moment via the corresponding equation of motion (see, e.g., Table I) using E(t + dt). Having calculated E(t) for all times, the dynamical equation is used to verify satisfaction of the tracking condition y(t) = Y (t).Since Eq.(1) has exactly the same structure of the single particle case, we will study systems with singleelectron excitation (i.e., N = 1) in one spatial dimension. In this case, Eq. (1) takes the formwhere −V (x) and A are specified in Table I for widely used models. The described scheme constitutes SDM, as the distinct physical systems in Fig. 1 produced the same Y (t), yet the resulting control fields calculated from Eq. (2) are unique once the system's initial state is supplied. The physical meaning of Eq. (2) is that a desired polarizability can be induced from any dynamical system as long as no constraints are imposed on the ...

We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.

This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first family of solutions describe the shape-preserving translation of a wavepacket along any desired trajectory in the x − y plane. In particular, we show that the dispersionless motion of a Gaussian wavepacket along both elliptical and circular paths can be achieved with rather simple electromagnetic field configurations. A second family of solutions involves a plane electromagnetic wave and a combination of generally inhomogeneous electric and magnetic fields. The novel analytical solutions of the Dirac equation given here provide important insights into the connection between the quantum relativistic dynamics of electrons and the underlying geometry of the Lorentz group.

This corrects the article DOI: 10.1103/PhysRevLett.119.173203.