اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRandom generators of Markovian evolution: A quantum-classical transition by superdecoherence
95
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of $N$-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighbouring eigenvalues through the complex spacing ratios and observe the horse-shoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives superdecoherence and supercoherification.
قيم البحث
اقرأ أيضاً
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a n
on-equilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target and the characteristic transport exponents.
We present explicit evaluations of quantum speed limit times pertinent to the Markovian dynamics of an open continuous-variable system. Specifically, we consider the standard setting of a cavity mode of the quantum radiation field weakly coupled to a
thermal bosonic reservoir. The evolution of the field state is ruled by the quantum optical master equation, which is known to have an exact analytic solution. Starting from a pure input state, we employ two indicators of how different the initial and evolved states are, namely, the fidelity of evolution and the Hilbert-Schmidt distance of evolution. The former was introduced by del Campo {em et al.} who derived a time-independent speed limit for the evolution of a Markovian open system. We evaluate it for this field-reservoir setting, with an arbitrary input pure state of the field mode. The resultant formula is then specialized to the coherent and Fock states. On the other hand, we exploit an alternative approach that employs both indicators of evolution mentioned above. Their rates of change have the same upper bound, and consequently provide a unique time-dependent quantum speed limit. It turns out that the associate quantum speed limit time built with the Hilbert-Schmidt metric is tighter than the fidelity-based one. As apposite applications, we investigate the damping of the coherent and Fock states by using the characteristic functions of the corresponding evolved states. General expressions of both the fidelity and the Hilbert-Schmidt distance of evolution are obtained and analyzed for these two classes of input states. In the case of a coherent state, we derive accurate formulas for their common speed limit and the pair of associate limit times.
The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and th
e $O(n)$-model in the limit $ntoinfty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $ntoinfty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.
We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a globally ordered
phase. We make this argument quantitatively precise by comparing different local and global indicators of classicality and quantumness, respectively in symmetry-breaking and symmetry-preserving quantum ground states. We first discuss how naively comparing local, pairwise entanglement and discord apparently leads to the opposite conclusion. Indeed, we show that in symmetry-preserving ground states the two-body entanglement captures only a modest portion of the total two-body quantum correlations, while, on the contrary, in maximally symmetry-breaking ground states it contributes the largest amount to the total two-body quantum correlations. We then put to test the conjecture by looking at the global, macroscopic correlation properties of quantum ground states. We prove that the ground states which realize the maximum breaking of the Hamiltonian symmetries, associated to a globally ordered phase, are the only ones that: I) are always locally convertible, i.e. can be obtained from all other ground states by only applying LOCC transformations (local operations and classical communication), while the reverse is never possible; II) minimize the monogamy inequality on the globally shared, macroscopic bipartite entanglement.
We consider a random walk on the fully-connected lattice with $N$ sites and study the time evolution of the number of distinct sites $s$ visited by the walker on a subset with $n$ sites. A record value $v$ is obtained for $s$ at a record time $t$ whe
n the walker visits a site of the subset for the first time. The record time $t$ is a partial covering time when $v<n$ and a total covering time when $v=n$. The probability distributions for the number of records $s$, the record value $v$ and the record (covering) time $t$, involving $r$-Stirling numbers, are obtained using generating function techniques. The mean values, variances and skewnesses are deduced from the generating functions. In the scaling limit the probability distributions for $s$ and $v$ lead to the same Gaussian density. The fluctuations of the record time $t$ are also Gaussian at partial covering, when $n-v={mathrm O}(n)$. They are distributed according to the type-I Gumbel extreme-value distribution at total covering, when $v=n$. A discrete sequence of generalized Gumbel distributions, indexed by $n-v$, is obtained at almost total covering, when $n-v={mathrm O}(1)$. These generalized Gumbel distributions are crossing over to the Gaussian distribution when $n-v$ increases.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
