相关论文: Conditional displacement operator for traveling fi…

We argue for an operational requirement that all state-dependent measures of disturbance should satisfy. Motivated by this natural criterion, we prove that in any $d$-dimensional Hilbert space and for any pair of non-commuting operators,…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and…

We consider the differential of a self-consistent transfer operator at a fixed point of the operator itself and show that its spectral properties can be used to establish a kind of local exponential convergence to equilibrium: probability…

We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…

We consider a Dirac operator with a dislocation potential on the real line. The dislocation potential is a fixed periodic potential on the negative half-line and the same potential but shifted by real parameter $t$ on the positive…

We determine necessary and sufficient conditions on the ring of differential operators of a finite purely inseparable field extension of positive characteristic for determining whether the extension is modular.

Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a…

We prove a conditional Wegner estimate for Schr\"odinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such…

We propose a scheme allowing a conditional implementation of suitably truncated general single- or multi-mode operators acting on states of traveling optical signal modes. The scheme solely relies on single-photon and coherent states and…

It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the…

In this thesis, we establish a necessary and sufficient condition for a weighted composition operator to commute with a self-adjoint weighted composition operator on the Fock space, then obtain a sufficient condition for these commuting…

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…

In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple…

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…

We provide a precise coupling of the finite circular beta ensembles and their limit process via their operator representations. We prove explicit bounds on the distance of the operators and the corresponding point processes. We also prove…

The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to…

We propose an experimentally feasible scheme to achieve directional transport of Rydberg excitations and entangled states in atomic arrays with unequal spacings. By leveraging distance-dependent Rydberg-Rydberg interactions and temporally…

We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential. It is vary important…

We formulate the theory of electron transport through coupled-quantum dots by extending the auxiliary operator representation. By using the generating functional technique, we derive the exact expressions for currents, dot-occupation…