相关论文: The Conditional Probability Interpretation of the …

This paper addresses the properties of Continuous Interior Penalty (CIP) finite element solutions for the Helmholtz equation. The $h$-version of the CIP finite element method with piecewise linear approximation is applied to a…

We explore methods to generate quantum coherence through unitary evolutions, by introducing and studying the coherence generating capacity of Hamiltonians. This quantity is defined as the maximum derivative of coherence that can be achieved…

The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian…

Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite…

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local…

Let $\mathcal K$ be an imaginary quadratic field. Let $\Pi$ and $\Pi'$ be irreducible generic cohomological automorphic representation of $GL(n)/{\mathcal K}$ and $GL(n-1)/{\mathcal K}$, respectively. Each of them can be given two natural…

We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…

We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…

In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…

Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different…

We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…

We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…

In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics - namely that the state of a particle is merely an expression of…

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented…

One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…

Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…

Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…

Computations of quantum corrections to the CMB spectrum and to scalar field dynamics during inflation very often take advantage of the "semi-classical" approach, where the metric fluctuations are simply omitted. On the other hand, a…

The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…