A room temperature CO2_2 line list with ab initio computed intensities

Atmospheric carbon dioxide concentrations are being closely monitored by remote sensing experiments which rely on knowing line intensities with an uncertainty of 0.5% or better. We report a theoretical study providing rotation-vibration line intensities substantially within the required accuracy based on the use of a highly accurate {\it ab initio} dipole moment surface (DMS). The theoretical model developed is used to compute CO$_2$ intensities with uncertainty estimates informed by cross comparing line lists calculated using pairs of potential energy surfaces (PES) and DMS's of similar high quality. This yields lines sensitivities which are utilized in reliability analysis of our results. The final outcome is compared to recent accurate measurements as well as the HITRAN2012 database. Transition frequencies are obtained from effective Hamiltonian calculations to produce a comprehensive line list covering all $^{12}$C$^{16}$O$_2$ transitions below 8000 cm$^{-1}$ and stronger than 10$^{-30}$ cm / molecule at $T=296$~

Deformation of intrasalt beds recorded by magnetic fabrics

Funding Information Israel Science Foundation (ISF). Grant Number: 868/17 Israeli Government. Grant Number: 40706 Israel Science Foundation. Grant Number: 868/17Peer reviewedPublisher PD

Simultaneous measurement of coordinate and momentum on a von Neumann lattice

It is shown that on a finite phase plane the $kq$-coordinates and the sites of a von Neumann lattice are conjugate to one another. This elementary result holds when the number $M$ defining the size of the phase plane can be expressed as a product, $M=M_{1}M_{2}$, with $M_{1}$ and $M_{2}$ being relatively prime. As a consequence of this result a hitherto unknown wave function is defined giving the probability of simultaneously measuring the momentum and coordinate on the von Neumann lattice.Comment: Published in EPL 83 (2008) 1000

Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result

In this paper we prove that any multi-resolution analysis of \Lc^2(\R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.Comment: Submitted to Journal Mathematical Physisc

Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.Comment: 4 pages, 3 figure

Dynamic Localization in Quantum Wires

In the paper the dynamic localization of charged particle (electron) in a quantum wire under the external non-uniform time-dependent electric field is considered. The electrons are trapped in a deep 'dynamic' quantum wells which are the result of specific features of the potential imposed on 2D electron gas: the scale of spatial nonuniformity is much smaller then the electron mean free path (L_1 << \bar{l}) and the frequency is much greater then \tau^{-1}, where \tau is the electron free flight time. As a result, the effect of this field on the charged particle is in a sense equivalent to the effect of a time-independent effective potential, that is a sequence of deep 'dynamic' quantum wells were the elelctrons are confined. The possible consequeces of this effect are also discussed and similarity with the classical Paul traps are emphasized.Comment: 21 pages, 1 figur

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase

Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice {\ee Z}_{D} \times {\ee Z}_{D} with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the algebraic formulation of the quantum phase problem. Certain equivalence classes in the space of labels are identified within each subalgebra, and connections with area-preserving canonical transformations are examined. The generalized representations of the Wigner function are examined in the finite-dimensional cyclic Schwinger basis. These representations are shown to conform to all fundamental conditions of the generalized phase space Wigner distribution. As a specific application of the Schwinger basis, the number-phase unitary operator pair in {\ee Z}_{D} \times {\ee Z}_{D} is studied and, based on the admissibility of the underlying q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum phase operator is established. This being the focus of this work, connections with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well as standard action-angle Wigner function formalisms are examined in the infinite-period limit. The concept of continuously shifted Fock basis is introduced to facilitate the Fock space representations of the Wigner function.Comment: 19 pages, no figure

Orthogonal localized wave functions of an electron in a magnetic field

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.Comment: RevTex, 18 pages, 5 ps fi