相关论文: Determinism plus chance in random matrix theory

Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…

We explore connections between homotopy type theory and information theory through homotopy cardinality. We define probability types and random variable types, prove that homotopy cardinality respects dependent sums under truncation and…

The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…

Consider Plurality with random tie-breaking. This paper uses standard axiomatic extensions of preferences over elements to preferences over sets (Kelly, Gardenfors, Responsiveness) to characterize all better-replies of a voter under…

We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…

We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of…

Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a…

One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched…

Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle(trajectories) and the Huygens principle…

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two-…

We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of $\hbar $. Considering $\hbar $ as a running parameter, a differential equation connecting two diagonalization processes for…

We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…

The Hamiltonian analysis for the linearized $\lambda R$ gravity plus a Chern-Simons term is performed. The first-class and second-class constraints for arbitrary values of $\lambda$ are presented, and one physical degree of freedom is…

One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true…

The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…

For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…

We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables correspond to the equations governing the activation dynamics…

We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…