相关论文: Modification of Crum's Theorem for `Discrete' Quan…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

Quantum simulations of electronic structure with a transformed Hamiltonian that includes some electron correlation effects are demonstrated. The transcorrelated Hamiltonian used in this work is efficiently constructed classically, at…

We carry out a Dirac sea reinterpretation of a discretized version of the Hamiltonian of quantum electrodynamics (QED), and analyze the perturbed vacuum in the continuum limit. We argue that if certain operators can be shown to be the…

With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…

We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…

In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…

In this paper we provide an action related to a certain sector of general relativity where the algebra of Hamiltonian constraints forms a first class system. This action is a Dirac-consistent stand-alone action with two physical degrees of…

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on $SL(2, \Real)$. The classical reduced system consists of a pair of Liouville…

The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of…

Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also {\it constraint equations}. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The…

The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration $\tau$ is upper bounded by $C/\tau$ for some positive…

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities.…

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…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths…

For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…

In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum…

Quantum systems unfold diversified correlations which have no classical counterparts. These quantum correlations have various different facets. Quantum entanglement, as the most well known measure of quantum correlations, plays essential…

Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be…