Related papers: Another look at qualitative properties of eigenval…
We study the well-posedness of Hamilton-Jacobi-Bellman equations on subsets of $\mathbb{R}^d$ in a context without boundary conditions. The Hamiltonian is given as the supremum over two parts: an internal Hamiltonian depending on an…
Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
We introduce a Hamiltonian-based quantum feature extraction method that generates complex features via the dynamics of $k$-local many-body spins Hamiltonians, enhancing machine learning performance. Classical feature vectors are embedded…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…
Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantum mechanics is exact. But explicit formulas are non trivial…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…
Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
We show that a method proposed recently, based on the characteristic polynomial of an effective Hamiltonian, had been developed several years earlier by other authors in a clearer and more general way. We outline both implementations of the…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for…