Formulae for partial widths derived from the Lindblad equation

Selstø, Sølve

doi:10.1103/physreva.85.062518

Cited by 4 publications

(6 citation statements)

References 44 publications

(72 reference statements)

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“…The initial-value problem ( 20)-( 21) represents a continuous-time quantum walk, namely a quantum particle propagating on a chain, in the presence of a trap of strength Γ at the origin. The survival of a quantum particle subject to a complex optical potential [35][36][37][38] was analyzed in [39]. The factorization (19) shows that, in the present case, this non-Hermitian potential is equivalent to the more rigorous framework provided by the Lindblad equation that also includes the measurement process (see [40][41][42][43][44][45] for related approaches in the context of first detection time of a quantum walk).…”

Section: The Model and Some Exact Resultsmentioning

confidence: 99%

“…The initial-value problem (20) and (21) represents a continuous-time quantum walk, namely a quantum particle propagating on a chain, in the presence of a trap of strength Γ at the origin. The survival of a quantum particle subject to a complex optical potential [36][37][38][39] was analyzed in [40]. The factorization (19) shows that, in the present case, https://doi.org/10.1088/1742-5468/ab4e8e…”

Section: Free Fermions On Z With a Sourcementioning

confidence: 88%

“…This integral can be expressed through the Laplace transform S 0 (s), given in (63), via the Parseval-Plancherel identity (37). Hence, to have more manageable results, one needs to compute Φ d (s) explicitly to obtain an integral representation comparable to (38).…”

Section: General Formalismmentioning

confidence: 99%

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Free fermions with a localized source

2019

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We analyze the time evolution of an open quantum system driven by a localized source of bosons. We consider non-interacting identical bosons that are injected into a single lattice site and and perform a continuous time quantum walks on a lattice. We show that the average number of bosons grows exponentially with time when the input rate exceeds a certain lattice-dependent critical value. Below the threshold, the growth is quadratic in time, which is still much faster than the naive linear in time growth. We compute the critical input rate for hyper-cubic lattices and find that it is positive in all dimensions d except for d = 2 where the critical input rate vanishes-the growth is always exponential in two dimensions. To understand the exponential growth, we construct an explicit microscopic Hamiltonian model which gives rise to the open system dynamics once the bath is traced out. Exponential growth is identified with a region of dynamic instability of the Hamiltonian system.

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Section: The Model and Some Exact Resultsmentioning

confidence: 99%

Section: Free Fermions On Z With a Sourcementioning

confidence: 88%

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Free fermions with a localized source

2019

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“…In the present framework, the effective description of the trap by an optical potential can be derived by first representing the trap as a zero-temperature phonon bath and then tracing out the degrees of freedom of the bath [27,[30][31][32][33]. A more formal approach is based on deriving a Lindblad dynamics for the particle coupled to the bath [63][64][65]. We again assume that the particle is launched at site a ≥ 0 at time t = 0.…”

Section: A Quantum Particlementioning

confidence: 99%

Survival of Classical and Quantum Particles in the Presence of Traps

2014

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We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. As a general rule, static traps are far less efficient to absorb quantum particles than classical ones. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.

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“…2.1.3 that, for certain types of L, a subspace of the system undergoes exactly the evolution generated by K and the recycling term merely takes one out of that subspace. There also exist methods to extend a given K into full Lindblad form [58,261]. Such methods, and Lindbladians in general, may be useful as phenomenological models of resonance decay [122].…”

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confidence: 99%

Lindbladians with multiple steady states: theory and applications

Albert¹

2018

Preprint

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Lindbladians with multiple steady states: theory and applications Victor V. Albert 2017Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered environment can drive the system toward exotic phases of matter or toward subspaces protected from noise. These cases often require the Lindbladian to have more than one steady state, and such Lindbladians are dissipative analogues of Hamiltonians with multiple ground states. This thesis studies Lindbladian extensions of topics commonplace in degenerate Hamiltonian systems, providing examples and historical context along the way.An important property of Lindbladians is their behavior in the limit of infinite time, and the first part of this work focuses on deriving a formula for the asymptotic projection -the map corresponding to infinite-time Lindbladian evolution. This formula is applied to determine the dependence of a system's steady state on its initial state, to determine the extent to which decay affects a system's linear or adiabatic response, and to determine geometrical structures (holonomy, curvature, and metric) associated with adiabatically deformed steady-state subspaces. Using the asymptotic projection to partition the physical system into a subspace free from nonunitary effects and that subspace's complement (and making a few other minor assumptions), a Dyson series is derived to all orders in an arbitrary perturbation. The terms in the Dyson series up to second order in the perturbation are shown to reproduce quantum Zeno dynamics and the effective operator formalism.

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Formulae for partial widths derived from the Lindblad equation

Cited by 4 publications

References 44 publications

Free fermions with a localized source

Free fermions with a localized source

Survival of Classical and Quantum Particles in the Presence of Traps

Lindbladians with multiple steady states: theory and applications

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