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bstract
The dynamics when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system can be understood as a combination of early time quantum ...correlation (von Neumann entropy) gain and late time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain, even though equilibrium thermodynamics does not apply. This energy increase is of quantum origin and results from the collective binding energy between the two systems. Counter-intuitively, this implies that also the hotter of the two systems generically experiences an initial energy increase when brought into contact with the other colder system. In the limit where the energy relaxation overwhelms the (quantum) correlation build-up, classical energy dynamics emerges where the energy in the hot system decreases immediately upon contact with a cooler system. We use both strongly correlated SYK systems and weakly correlated mixed field Ising chains to exhibit these characteristics, and comment on its implications for both black hole evaporation and quantum thermodynamics.
We calculate the current-voltage (I−V) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The ...phase ϕ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I−V characteristic. The number of voltage steps counts the number of Rabi oscillations per 2π increment of ϕ, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the Majorana-induced DC Shapiro steps in topological Josephson junctions of Choi et al. Phys. Rev. B 102, 140501(R) (2020)-but now for a nontopological Andreev qubit.
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g., quantum dot, with interactions strong enough to completely washout quasiparticle ...excitations in the infrared. In this paper we consider the complex-valued SYK model at initial temperature T and chemical potential μ coupled to a large reservoir by a quench at time t = 0 . The reservoir is kept at zero temperature and charge neutrality. We find that the dynamics of the discharging process of the SYK quantum dot reveals a distinctive characteristic of the SYK non-Fermi liquid (nFl) state. In particular, we focus on the tunneling current induced by the quench. We show that the temperature dependent contribution to the current's half-life scales linearly in T at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as T2.
The Planckian relaxation rate ℏ/tP = 2πkBT sets a characteristic timescale for both the equilibration of quantum critical systems and maximal quantum chaos. In this Rapid Communication, we show that ...at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap Δ behaves as ηℏ/tP at low temperatures, where η is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite Δ domain is settled between the two critical temperatures.
We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the beta-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue ...recently raised by Cheipesh, Cheianov, and Boyarsky Phys. Rev. D 104, 116004 (2021), and discuss the relevant timescales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.
Detection of the fusion rule of Majora na zero‐modes is a near‐term milestone on the road to topological quantum computation. An obstacle is that the non‐deterministic fusion outcome of topological ...zero‐modes can be mimicked by the merging of non‐topological Andreev levels. To distinguish these two scenarios, the dynamical signatures of the ground‐state degeneracy that is the defining property of non‐Abelian anyons is searched for. By adiabatically traversing parameter space along two different pathways, one can identify ground‐state degeneracies from the breakdown of adiabaticity. It is shown that the approach can discriminate against accidental degeneracies of Andreev levels.
A demonstration of the fusion rule of Majorana zero‐modes would be a milestone in the development of a topological quantum computer. An obstacle is that the non‐deterministic fusion outcome can be mimicked by trivial Andreev levels. Here, it is shown that one can distinguish these by adiabatically traversing parameter space along two different pathways of coupling and decoupling operations.
We consider non-equilibrium dynamics of two initially independent reservoirs \(A\) and \(B\) filled with a cold Fermi gas coupled and decoupled by two quantum quenches following one another. We find ...that the von Neumann entropy production induced by the quench is faster than thermal transport between the reservoirs and defines the short-time dynamics of the system. We analyze the energy change in the system which adds up the heat transferred between \(A\) and \(B\) and the work done by the quench to uncouple the reservoirs. In the case when \(A\) and \(B\) interact for a short time, we notice an energy increase in both reservoirs upon decoupling. This energy gain results from the quench's work and does not depend on the initial temperature imbalance between the reservoirs. We relate the quench's work to the mutual correlations of \(A\) and \(B\) expressed through their von Neumann entropies. Utilizing this relation, we show that once \(A\) and \(B\) become coupled, their entropies grow (on a timescale of the Fermi time) faster than the heat flow within the system. This result may provide a track of quantum correlations' generation at finite temperatures which one may probe in ultracold atoms, where we expect the characteristic timescale of correlations' growth to be \(\sim 0.1 {\rm ms}\).
The dynamics when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system can be understood as a combination of early time quantum correlation (von ...Neumann entropy) gain and late time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain, even though equilibrium thermodynamics does not apply. This energy increase is of quantum origin and results from the collective binding energy between the two systems. Counter-intuitively, this implies that also the hotter of the two systems generically experiences an initial energy increase when brought into contact with the other colder system. In the limit where the energy relaxation overwhelms the (quantum) correlation build-up, classical energy dynamics emerges where the energy in the hot system decreases immediately upon contact with a cooler system. We use both strongly correlated SYK systems and weakly correlated mixed field Ising chains to exhibit these characteristics, and comment on its implications for both black hole evaporation and quantum thermodynamics.
We calculate the current-voltage (I-V) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The ...phase \(\phi\) across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I-V characteristic. The number of voltage steps counts the number of Rabi oscillations per \(2\pi\) increment of \(\phi\), providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the "Majorana-induced DC Shapiro steps in topological Josephson junctions" of Phys. Rev. B 102, 140501(R) (2020) -- but now for a non-topological Andreev qubit.
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