Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

Domino mechanisms in photoinduced phase transitions

Photoinduced structural phase transitions via excited electronic states are discussed theoretically using a one-dimensional model composed of localized electrons and lattices under the adiabatic or diabatic approximation. We show that the global structural change by photoexcitation only at a site is possible, and we clarify conditions for the occurrence of such phenomena. Spatiotemporal dynamics of nonequilibrium first-order phase transitions is also investigated in detail in terms of photoinduced nucleations and domino processes of the domain boundaries (domain walls), which are in striking contrast to the mean-field dynamics. In the adiabatic regime, after the spontaneous emission of a photon, an initial local structural change (i) remains locally, (ii) induces cooperatively a global structural change, or (iii) disappears and returns to the initial phase. Dynamical features of the case (ii) are characterized by the deterministic (semichaotic) domino process; domain walls between the two phases move determinis-tically at a constant velocity (with changing speed) without further spontaneous emissions in the case of strong (weak) dissipation. In the diabatic regime, similar three types of structural change exist. The domain-wall dynamics is described as the stochastic domino process, which is accompanied by the successive radiative transitions. A new theoretical treatment is also proposed to study crossover between the adiabatic and diabatic regimes.     

Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems

The Born–Oppenheimer treatment leads to the adiabatic framework where the non-adiabatic terms are the physical entities responsible for the coupling between adiabatic states. The main disadvantage of this treatment is in the fact that these coupling terms frequently become singular thus causing difficulties in solving the relevant Schroedinger equation for the motion of the nuclei that make up the molecular systems. In this review, we present the line integral approach which enables the formation of the adiabatic-to-diabatic transformation matrix that yields the friendlier diabatic framework. The review concentrates on the mathematical conditions that allow the rigorous derivation of the adiabatic-to-diabatic transformation matrix and its interesting physical properties. One of the findings of this study is that the non-adiabatic coupling terms have to be quantized in a certain manner in order to yield single-valued diabatic potentials. Another important feature revealed is the existence of the topological matrix, which contains all the topological features of a given molecular system related to a closed contour in configuration space. Finally, we present an approximation that results from the Born–Oppenheimer treatment which, in contrast to the original Born–Oppenheimer approximation, contains the effect of the non-adiabatic coupling terms. The various derivations are accompanied by examples which in many cases are interesting by themselves.     

Bifurcation analysis of the sixteen-vertex model

We shall construct a hierarchy of subclasses of the 16-vertex model having qualitatively different symmetry properties. We determine the bifurcation points in the parameter space of the model where new symmetry elements are added to the invariance group of the partition function. In this paper we restrict ourselves to the study of site-dependent transformations converting a homogeneous 16-vertex model into a different homogeneous model. Apart from a trivial transformation, resulting in a change of sign of all vertex weights, such site-dependent transformations exist only for those points in parameter space where particular relations are satisfied. The solution of these relations gives rise to three 6-parameter families of models, two of which are equivalent to the general 8-vertex model, and two families of 4-parameter models. The primary bifurcation models depending on six parameters contain three different types of secondary bifurcation models, depending on 4 parameters, one of which is equivalent to Baxter's symmetric 8-vertex model.     

Optimal and covariant single-copy LOCC transformation between two two-qubit states

Given two two-qubit pure states characterized by their Schmidt numbers we investigate an optimal strategy to convert the states between themselves with respect to their local unitary invariance. We discuss the efficiency of this transformation and its connection to LOCC convertibility properties between two single-copy quantum states. As an illustration of the investigated transformations we present a communication protocol where in spite of all expectations a shared maximally entangled pair between two participants is the worst quantum resource.     

Spectroscopic study of phase transformations between orthorhombic and tetragonal C60 polymers

We present a detailed study of transformations between the orthorhombic and tetragonal polymeric states of C₆₀. The transformations are characterised by Raman spectroscopy and X-ray diffraction. We show that the transformation from the orthorhombic (O) phase to the tetragonal (T) phase is very fast and our results indicate that the transformation goes via an intermediate dimer (D) state in a two-stage process, O↦D and, D↦T transformations, where the second process is slower than the first. On the other hand, the transformation from the tetragonal to the orthorhombic phase is significantly slower, indicating a high-energy threshold to break the polymer bonds at the temperatures used. The results also support earlier suggestions that the tetragonal phase contains disordered dimers that can be viewed as lattice defects in the formation of higher polymers.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

利用旋转波片组实现偏振变换器的两种新方法

偏振变换器作为一种重要的光学器件．以其高偏振变换精度、低成本、低插入损耗以及控制算法简单的特性在相干光纤通信和高速光纤通信领域具有十分重要的地位。提出了利用两个λ／4波片和一个λ／2波片的三波片组合实现任意偏振态变换的新方法。用改进的三维庞加莱球方法—偏振态投射平面的二维几何方法分别推导出了λ／4 λ／4 λ／2组合以及λ／2 λ／4 λ／4组合实现任意偏振态变换时每个波片的位置参量计算公式。研究结果表明：两个λ／4波片和一个λ／2波片的任意组合都可以实现任意偏振态的变换;用偏振态投射平面的几何方法处理偏振变换的相关问题比庞加莱球方法和矩阵处理方法简洁明了。研究结果为偏振变换器的设计提供了理论依据。     

Theory of the Domino Dynamics Via Nonadiabatic Transitions

Photoinduced nucleation processes, called photoinduced domino processes, via excited electronic states are discussed theoretically for a one-dimensional arrangement of deformable molecules using a model composed of localized electrons and lattices. We show that the global structural transition by photoexcitation only at a molecule (site) is possible in the adiabatic and diabatic limits. An intermediate regime between these limits is investigated; an analytical treatment and a numerical calculation are presented taking into account the nonadiabatic electronic transition, i . e ., the Landau-Zener-type transition. In this regime, the domino dynamics can be terminated halfway ( i . e ., a finite - size domain appears) in contrast to the "all-or-nothing" domino dynamics ( i . e ., a photoinduced domain vanishes or grows up to the system size) in the adiabatic and diabatic limits.     

Study of Two-Mode Squeezed Magnetopolarons

In this paper, we conduct an investigation into two-dimensional squeezed magnetopolarons. The Hamiltonian of magnetopolarons is dealt with two-mode squeezed states transformation, which is based on the Lee-Low-Pines and Huybrechts （LLP-H） canonical transformations. This method makes it possible to take account of the linear terms, bilinear ones of phonon operators, and the correlation between two longitudinal optical （LO） phonon modes. The energies of the ground state and excited states are evaluated by variational approach, and accurate results are obtained. Furthermore, the renormalized cyclotron masses for some possible transitions are discussed in detail.     

Catalysis of entanglement manipulation for mixed states

We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.     

Constrained relativistic mean-field approach with fixed configurations

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean-field model. As an example, the potential energy surfaces of ²⁰⁸Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till the very deformed region, and to obtain several well-defined deformed excited states which can hardly be expected from the adiabatic PESs.     

The I2(B) predissociation by solving an inverse atoms-in-molecule problem

The valence electronic states of the iodine molecule are analysed by means of a simple atoms-in-molecule model which accounts for the lowest ²P states of iodine atoms and approximates the spin-orbit interaction by its atomic part. For this model, an inverse problem is solved, i.e. non-relativistic potential energy curves and diabatic couplings are determined by a least-squares fit to known relativistic potential energy curves. The resulting adiabatic wave functions are used to calculate the electronic matrix elements responsible for natural, hyperfine and magnetic predissociation of the iodine molecule in the B0⁺ _u: state. The results are in reasonable agreement with experimental data, being stable enough with respect to the variation of input relativistic potentials. They also indicate the importance of diabatic couplings between the non-relativistic states of the same symmetry.     

Inter-state coupling and definitions of bright and dark states

Contrary to a standard definition of diabatic states (i.e., those without momentum-dependent coupling), based on the construction from adiabatic ones, we defined diabatic states as bright and dark states of a given experiment. Namely, they are defined as states providing maximum, respectively, zero value of electronic transition dipole moments projected to a given polarization vector. Second, the state from (or to) which the optical transition is performed is not from the space of investigated electronic excited state manifold, but it is chosen by the observer. It is shown, for this case, that the inter-state coupling is a general function of vibrational coordinates. The explicit dependence of the inter-state coupling on vibrational coordinates is particularly important for system with strong Stokes shift. The role of exact definitions of bright and dark states as well as the inter-state coupling is discussed with respect to the coherent structure of electronic population observed in optical spectroscopy.     

Super-gauge transformations on the six-dimensional hypercone

Super-gauge transformations on physical space-time are defined on the projective six-dimensional hypercone. The basic observation which motivates the present approach is that the product of any two super-gauges is a general conformal (+ γ₅) transformation and indeed these latter transformations are simply realized on the six-dimensional hypercone. It turns out that also super-gauge transformations have a natural action on this projective space where the parameters of such transformations are (totally anticommuting) spinors which transform according to the fundamental (eight-dimensional) representation of the spinor group SU (2,2), isomorphic to the conformal group. The enlarged algebra of super-gauges, conformal and chiral transformations and its most relevant representations are discussed in the present formalism.     

Bound-bound state quantum wave packet dynamics in the intermediate coupling range: the A1Sigma+u (0+u) and b3IIu (0+u) system in Rb2

The real-time quantum dynamics of a wave packet confined to two coupled bound states at intermediate interaction strength is probed by experiment and calculations on the A1Sigma(+)(u) approximately b (3)II(u) system in Rb2 molecules. The general dynamics consists of rapid spreading out over the whole phase space. Particular conditions exist, however, under which the initial wave packet motion separates into two mesobatic trajectories with distinct frequencies. These diabatic or adiabatic hybrid trajectories are analogous to those responsible for longevity resonances in bound-unbound systems.     

Unitary renormalization of the Lee model Y4

The Lee model Y₄ is renormalized by unitary transformation. A norm convergent (in each sector) sequence of unitary dressing transformations, which transform a sequence of renormalized cut-off Hamiltonians to a sequence of operators converging strongly on a dense set of states, is defined. The self-adjointness and semiboundedness (in each sector) of the renormalized Hamiltonian are proved.     

Superposition in quantum and relativity physics—An interaction interpretation of special relativity theory: Part III

With the interaction interpretation, the Lorentz transformation of a system arises with selection from a superposition of its states in an observation-interaction. Integration of momentum states of a mass over all possible velocities gives the rest-mass energy. Static electrical and magnetic fields are not found to form such a superposition and are to be taken as irreducible elements. The external superposition consists of those states that are reached only by change of state of motion, whereas the internal superposition contains all the states available to an observer in a single inertial coordinate system. The conjecture is advanced that states of superposition may only be those related by space-time transformations (Lorentz transformations plus space inversion and charge conjugation). The continuum of external and internal superpositions is examined for various masses, and an argument for the unity of the super-positions is presented.     

CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART II: ELEMENTARY STRUCTURE-PRESERVING TRANSFORMATIONS

It has been shown in a previous paper that there is a real-valued transformation from the generalN -degree-of-freedom second order system to a second order system characterized by diagonal matrices. An immediate extension of this fact is that for any second order system, there is a set of real-valued transformations (thestructure-preserving transformations) which transform this system to a different second order system having identical characteristic behaviour. There are several possible reasons why it may be very useful to achieve a particular structure in the transformed system. It is obvious that a diagonal structure is extremely useful and a method has been devised for determining the diagonalizing transformation from the solution of the usual (complex) eigenvalue-eigenvector problem.This paper begins by outlining the usefulness of some other structures. Then it defines a class of elementary structure-preserving co-ordinate transformations that transform from one N -degree-of-freedom second order system to another. The termelementary is applied because any one of these transformations is the minimum-rank modification of the identity transformation. The changes occurring in the system matrices as a result of the application of one such elementary transformation transpire to be very simple in form, they are low rank, and they can be computed very efficiently.This paper provides the fundamental tools to enable the design of structure-preserving co-ordinate transformations which transform a second order system originally characterized by three general matrices in stages into a mathematically similar second order system characterized by three diagonal matrices. The procedure by which the individual elementary transformations are obtained is still under development and it is not discussed in this paper. However, an illustration is given of a five-degree-of-freedom self-adjoint system being transformed into tridiagonal form.