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All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
Motivated by the fermion bag approach we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
This paper is concerned with the well-posedness analysis of the Hartree-Fock system modeling the time evolution of a quantum system comprised of fermions. We consider quantum states with finite mass and finite kinetic energy, and the…
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in…
Labourie raised the question of determining the possible asymptotics for the growth rate of compact $k$-surfaces, counted according to energy, in negatively curved $3$-manifolds, indicating the possibility of a theory of thermodynamical…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
Heisenberg time evolution under a chaotic many-body Hamiltonian $H$ transforms an initially simple operator into an increasingly complex one, as it spreads over Hilbert space. Krylov complexity, or `K-complexity', quantifies this growth…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic…
We consider the existence and H\"{o}lder continuity conditions for the $k$-th order derivatives of self-intersection local time for $d$-dimensional fractional Brownian motion, where $k=(k_1,k_2,\cdots, k_d)$. Moreover, we show a limit…
We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be…
There exists a Hamiltonian formulation of the factorisation problem which also needs the definition of a factorisation ensemble (a set to which factorable numbers, $N'=x'y'$, having the same trivial factorisation algorithmic complexity,…
Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in…