Related papers: Linear Growth of Circuit Complexity from Brownian …
We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing interactions of order two up to $L$, we…
We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either…
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
We construct a family of processes, from a single Poisson process, that converges in law to a complex Brownian motion. Moreover, we find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly…
We study quantum dynamics generated by time-dependent Hamiltonians in Krylov space, the minimal subspace in which the evolution takes place. We establish a direct link between dynamics in the time-dependent Krylov subspace and the…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…
We use the SYK family of models with $N$ Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free,…
We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a…
When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some prescribed value. This conditioning problem is well understood within the linear operator…
Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales…
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
Quantum many-body systems out of equilibrium pose some of the most intriguing questions in physics. Unfortunately, numerically keeping track of time evolution of states under Hamiltonian dynamics constitutes a severe challenge for all known…
We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an…
We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped…
We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…