Колебательно-вращательный спектр высокого разрешения в районе полос 3ν-=SUB=-4-=/SUB=-, ν-=SUB=-2-=/SUB=-+2ν-=SUB=-4-=/SUB=- и 2ν-=SUB=-2-=/SUB=-+ν-=SUB=-4-=/SUB=- молекулы -=SUP=-72-=/SUP=-GeH-=SUB=-4-=/SUB=-

The high-resolution spectrum of the 72GeH4 molecule was recorded on a Bruker IFS 125HR Fourier spectrometer with an optical resolution of 0.003 cm-1. The line positions were analyzed for ten interacting vibrational-rotational bands 3ν4 (1F2, F1, 2F2), v2+ 2ν4 (1E, F1, F2, 2E) and 2ν2+v4 (1F2, F1, 2F2) in the range 2350-2750 cm-1. As a result of the analysis, 1726 experimental lines were identified with the maximum value of the quantum number Jmax = 17; then used in the fitting procedure with parameters of the effective Hamiltonian. The resulting set of 35 spectroscopic parameters describes the vibrational-rotational structure of the spectrum with drms = 7.5 · 10-4 cm-1.

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights into the processes involved. We clarify that the form of the effective Hamiltonian depends on the field states considered, and consequently different expressions can be obtained, each of them with a well-defined range of validity and possible applications. We also apply our results to some specific cases, mainly the Lamb shift, the Casimir-Polder atom-surface interaction, and the dispersion interactions between atoms, molecules, or, in general, polarizable bodies.

Superconducting Proximity Effect in Magnetic Molecules

<p>We studied the transport through magnetic molecules (MM) coupled to superconducting (S), ferromagnetic (F) and normal (N) leads, with the aim of investigating the interplay between the magnetism and the superconducting proximity effect. The magnetic molecules were modeled using the Anderson model with an exchange coupling between the electron spins and the spin of the molecule. We worked in the infinite superconducting gap limit and treated the coupling between the molecule and the superconducting lead exactly, via an effective Hamiltonian. For the F/N-MM-S systems we used a real-time diagrammatic perturbation theory to calculate the electronic transport properties of the systems to first order in the tunnel coupling to the normal or ferromagnetic lead and then analysed the properties with respect to the parameters of these models. For these systems we found that the current maps out the excitation energies of the eigenstates of the effective Hamiltonian and that various parameters in these systems can lead to a negative differential conductance. In the N-MM-S case the current had no overall spin dependence, but when the normal lead is instead ferromagnetic there was a spin dependence and both the electronic and molecular spin expectation values could take on non-zero values. We also found that the polarisation of the ferromagnetic lead suppresses the superconducting proximity effect. Furthermore in the N-MM-S case the Fano factor indicated a transition from Poissonian transport of single electrons to Poissonian transport of electron pairs as the superconducting proximity effect goes out of resonance, however in the F-MM-S case this did not occur. For the S-MM-S systems we calculated the equilibrium Josephson current and found that in the infinite superconducting gap limit no 0 − π transition was possible. Advantages of this study compared to related ones are that we allow for arbitrarily large Coulomb interactions and we take into account coupling to the superconducting lead non-perturbatively. This is however at the expense of working in the superconducting gap limit. Recently it has been possible to couple single molecules to superconducting leads. This study therefore aims to be indicative of the transport properties that will be observed in future experiments involving single magnetic molecules coupled to leads.</p>

Superconducting Proximity Effect in Magnetic Molecules

<p>We studied the transport through magnetic molecules (MM) coupled to superconducting (S), ferromagnetic (F) and normal (N) leads, with the aim of investigating the interplay between the magnetism and the superconducting proximity effect. The magnetic molecules were modeled using the Anderson model with an exchange coupling between the electron spins and the spin of the molecule. We worked in the infinite superconducting gap limit and treated the coupling between the molecule and the superconducting lead exactly, via an effective Hamiltonian. For the F/N-MM-S systems we used a real-time diagrammatic perturbation theory to calculate the electronic transport properties of the systems to first order in the tunnel coupling to the normal or ferromagnetic lead and then analysed the properties with respect to the parameters of these models. For these systems we found that the current maps out the excitation energies of the eigenstates of the effective Hamiltonian and that various parameters in these systems can lead to a negative differential conductance. In the N-MM-S case the current had no overall spin dependence, but when the normal lead is instead ferromagnetic there was a spin dependence and both the electronic and molecular spin expectation values could take on non-zero values. We also found that the polarisation of the ferromagnetic lead suppresses the superconducting proximity effect. Furthermore in the N-MM-S case the Fano factor indicated a transition from Poissonian transport of single electrons to Poissonian transport of electron pairs as the superconducting proximity effect goes out of resonance, however in the F-MM-S case this did not occur. For the S-MM-S systems we calculated the equilibrium Josephson current and found that in the infinite superconducting gap limit no 0 − π transition was possible. Advantages of this study compared to related ones are that we allow for arbitrarily large Coulomb interactions and we take into account coupling to the superconducting lead non-perturbatively. This is however at the expense of working in the superconducting gap limit. Recently it has been possible to couple single molecules to superconducting leads. This study therefore aims to be indicative of the transport properties that will be observed in future experiments involving single magnetic molecules coupled to leads.</p>

Endpoint relations for baryons

Following our earlier work we establish kinematic endpoint relations for baryon decays using the Wigner-Eckart theorem and apply them to $$ \frac{1}{2}\to \frac{1}{2} $$ 1 2 → 1 2 and $$ \frac{1}{2}\to \frac{3}{2} $$ 1 2 → 3 2 baryon transitions. We provide angular distributions at the kinematic endpoint which hold for the generic d = 6 model-independent effective Hamiltonian and comment on the behaviour in the vicinity of the endpoint. Moreover, we verify the endpoint relations, using an explicit form factor parametrisation, and clarify constraints on helicity-based form factors to evidence endpoint relations. Our results provide guidance for phenomenological parameterisations, consistency checks for theory computations and experiment. Results are applicable to ongoing and future new physics searches at LHCb, BES III and Belle II with rare semileptonic-, dineutrino-and charged-modes, which include Λb → Λ(*)ℓℓ, Λb → Λ(*)νν, Ωb → Ωℓℓ, Λc → pℓℓ, Σ → pℓℓ and Λb → $$ {\Lambda}_c^{\left(\ast \right)} $$ Λ c ∗ ℓν.

Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

Chebyshev matrix product states with canonical orthogonalization for spectral functions of strongly correlated systems

We propose a method to calculate the spectral functions of strongly correlated systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. We demonstrate for the first time that Chebyshev MPS can be used in quantum chemistry. We also caution the application for electron-phonon system with densed density of states.

Computing Effective Hamiltonians of Coupled Electromagnetic Systems

In this paper, we present an efficient procedure to compute the effective Hamiltonian matrix of a coupled electromagnetic system consisting of subsystems that are coupled to a discrete number of channels through couplers. Each subsystem is described by its own effective non-Hermitian Hamiltonian and the corresponding Quasi-normal Modes (QNMs), while the coupler connecting the subsystems and the channels is described by the scattering matrix, which is equivalent to the transfer matrix, in terms of port vectors defined for the coupler. Due to the constraints imposed by the QNMs of the subsystems and the wave dynamics of the channels, as well as boundary condition constraints, constraint-free port vectors need to be chosen efficiently and they follow two rules: 1) port vectors forming loops with couplers; 2) port vectors of couplers with most constraints or with less freedom. With the constraint-free port vectors chosen, the effective Hamiltonian matrix of the coupled electromagnetic system can be obtained by imposing the boundary condition constraints. After the effective Hamiltonian is obtained, the eigenvalues, eigenvectors and dispersion relation of the coupled electromagnetic system, as well as other quantities such as the reflection and transmission, can be calculated. A 2D interstitial square coupled MRRs array is used as an example to demonstrate the computational procedure. The computation of the effective Hamiltonian matrix of a coupled electromagnetic system has many potential applications such as MRRs array, coupled Parity-Time Non-Hermitian electromagnetic system, as well as the dispersion relation of finite and infinite arrays.