We investigate the properties of a quantum walk which can simulate the behavior of a spin 1/2 particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry ...between two branes. Such a setup constitutes a Formula: see text dimensional version of the Randall-Sundrum model, which plays an important role in high energy physics. In the continuum spacetime limit, the quantum walk reproduces the Dirac equation corresponding to the model, which allows to anticipate some of the properties that can be reproduced by the quantum walk. In particular, we observe that the probability distribution becomes, at large time steps, concentrated near the "low energy" brane, and can be approximated as the lowest eigenstate of the continuum Hamiltonian that is compatible with the symmetries of the model. In this way, we obtain a localization effect whose strength is controlled by a warp coefficient. In other words, here localization arises from the geometry of the model, at variance with the usual effect that is originated from random irregularities, as in Anderson localization. In summary, we establish an interesting correspondence between a high energy physics model and localization in quantum walks.
Abstract
We propose a nonlinear quantum walk model inspired in a photonic implementation in which the polarization state of the light field plays the role of the coin-qubit. In particular, we take ...profit of the nonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows to implement a nonlinear coin operator, one that depends on the state of the coin-qubit. We consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us to gain some insight into the existence of different solitonic structures, such as bright and dark solitons. We illustrate several properties of these solitons with numerical calculations, including the effect on them of an additional phase simulating an external electric field.
Abstract
In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma ...from stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from 10−14 to 10−9 M⊙ yr−1. The spatial jet evolution covers ∼500 pc from jet injection in the grid at 10 pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that toroidal magnetic fields can prevent fast jet expansion and the subsequent embedding of further stars via magnetic tension. In this sense, magnetic fields avoid a runaway deceleration process. Furthermore, when the mass-load is large enough to increase the jet density and produce fast, differential jet expansion, the conversion of magnetic energy flux into kinetic energy flux (i.e., magnetic acceleration), helps to delay the deceleration process with respect to non-magnetised jets. We conclude that the typical stellar population in elliptical galaxies cannot explain jet deceleration in classical FRI radio galaxies. However, we observe a significant change in the jet composition, thermodynamical parameters and energy dissipation along its evolution, even for moderate values of the mass-load.
The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such ...scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.
Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a ...phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.
We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin ...operator, with an angle which depends (in a nonlinear fashion) on the state of the walker. This simple dependence makes it easy to consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us, under some approximations, to gain some insight into the nature of soliton structures, which is illustrated by our numerical calculations. These solitons are stable structures whose trajectories can be modulated by choosing the appropriate initial conditions. We have also studied the stability of solitons when they are subject to an additional phase that simulates an external electric field, and also explored if they are formed in higher dimensional spaces.
We investigate the properties of a quantum walk which can simulate the behavior of a spin \(1/2\) particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry ...between two branes. Such a setup constitutes a \(1+1\) dimensional version of the Randall-Sundrum model, which plays an important role in high energy physics. In the continuum spacetime limit, the quantum walk reproduces the Dirac equation corresponding to the model, which allows to anticipate some of the properties that can be reproduced by the quantum walk. In particular, we observe that the probability distribution becomes, at large time steps, concentrated near the "low energy" brane, and can be approximated as the lowest eigenstate of the continuum Hamiltonian that is compatible with the symmetries of the model. In this way, we obtain a localization effect whose strength is controlled by a warp coefficient. In other words, here localization arises from the geometry of the model, at variance with the usual effect that is originated from random irregularities, as in Anderson localization. In summary, we establish an interesting correspondence between a high energy physics model and localization in quantum walks.
In this paper we present steady-state RMHD simulations that include a mass-load term to study the process of jet deceleration. The mass-load mimics the injection of a proton-electron plasma from ...stellar winds within the host galaxy into initially pair plasma jets, with mean stellar mass-losses ranging from \(10^{-14}\) to \(10^{-9}\,{M_\odot\,yr^{-1}}\). The spatial jet evolution covers \(\sim 500\,{\rm pc}\) from jet injection in the grid at 10~pc from the jet nozzle. Our simulations use a relativistic gas equation of state and a pressure profile for the ambient medium. We compare these simulations with previous dynamical simulations of relativistic, non-magnetised jets. Our results show that toroidal magnetic fields can prevent fast jet expansion and the subsequent embedding of further stars via magnetic tension. In this sense, magnetic fields avoid a runaway deceleration process. Furthermore, when the mass-load is large enough to increase the jet density and produce fast, differential jet expansion, the conversion of magnetic energy flux into kinetic energy flux (i.e., magnetic acceleration), helps to delay the deceleration process with respect to non-magnetised jets. We conclude that the typical stellar population in elliptical galaxies cannot explain jet deceleration in classical FRI radio galaxies. However, we observe a significant change in the jet composition, thermodynamical parameters and energy dissipation along its evolution, even for moderate values of the mass-load.
The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such ...scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.
Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a ...phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: The diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.
PDF
