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A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital…
A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.
A first-order gauge invariant formulation for the two-dimensional quantum rigid rotor is long known in the theoretical physics community as an isolated peculiar model. Parallel to that fact, the longstanding constraints abelianization…
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…
This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with…
The high degree of symmetry renders the dynamics of cosmological as well as some black hole spacetimes describable by a system of finite degrees of freedom. These systems are generally known as minisuperspace models. One of their important…
A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as…
We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem,…
With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…