Free Bosons with a Localized Source

Abstract

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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Cited by in corpus (16)

• Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
• Universality in driven open quantum matter
• Unbounded entanglement production via a dissipative impurity
• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
• Diagrammatic Monte Carlo for Dissipative Quantum Impurity Models
• Kondo-Zeno crossover in the dynamics of a monitored quantum dot
• Controlling superfluid flows using dissipative impurities
• Exact density profile in a tight-binding chain with dephasing noise
• Quantum wires with local particle loss: Transport manifestations of fluctuation-induced effects
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Random walk through a fertile site
• Shape effects of localized losses in quantum wires: dissipative resonances and nonequilibrium universality
• Loss-induced quantum information jet in an infinite temperature Hubbard chain
• Dissipative Kondo physics in the Anderson Impurity Model with two-body losses