Physics beyond quasi-particles: Spectrum and completeness of the 3 state superintegrable chiral Potts model

We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitations is compared with the BCS superconductivity spectrum and the counting rules are compared with the closely related $S=1$ XXZ spin chain.Comment: 39 page

Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z_3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z_3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1

Spin operator matrix elements in the superintegrable chiral Potts quantum chain

We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur

Multi-particle structure in the Z_n-chiral Potts models

We calculate the lowest translationally invariant levels of the Z_3- and Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating N to infinity. In the high-temperature massive phase we find that the pattern of the low-lying zero momentum levels can be explained assuming the existence of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m_Q = Q m_1. Exponential convergence in N is observed for the single particle gaps, while power convergence is seen for the scattering levels. We also verify that qualitatively the same pattern appears for the self-dual and integrable cases. For general Z_n we show that the energy-momentum relations of the particles show a parity non-conservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi, where \phi is the chiral angle and Q is the Z_n-charge of the respective particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript), BONN-HE-92-3

An intense source for cold cluster ions of a specific composition

Funding Information: This work was supported by EFRE (K-Regio project FAENOMENAL, Grant No. EFRE 2016-4) and the Austrian Science Fund FWF (Project No. P31149, I4130). This work was also supported by Fundação para a Ciência e a Tecnologia (FCT-MCTES), Radiation Biology and Biophysics Doctoral Training Programme (RaBBiT, PD/00193/2012); Applied Molecular Biosciences Unit - UCIBIO (UIDB/04378/2020) and CEFITEC Unit (UIDB/00068/2020); and scholarship Grant No. PD/BD/114447/2016 to J.A., F. Zappa acknowledges support from the Brazilian agency CNPq. K.v.H. kindly acknowledges the award of a LFUI guest professorship.The demand for nanoscale materials of ultra-high purity and narrow size distribution is addressed. Clusters of Au, C60, H2O, and serine are produced inside helium nanodroplets using a combination of ionization, mass filtering, collisions with atomic or molecular vapor, and electrostatic extraction, in a specific and novel sequence. The helium droplets are produced in an expansion of cold helium gas through a nozzle into vacuum. The droplets are ionized by electron bombardment and subjected to a mass filter. The ionic and mass-selected helium droplets are then guided through a vacuum chamber filled with atomic or molecular vapor where they collide and "pick up" the vapor. The dopants then agglomerate inside the helium droplets around charge centers to singly charged clusters. Evaporation of the helium droplets is induced by collisions in a helium-filled radio frequency (RF)-hexapole, which liberates the cluster ions from the host droplets. The clusters are analyzed with a time-of-flight mass spectrometer. It is demonstrated that using this sequence, the size distribution of the dopant cluster ions is distinctly narrower compared to ionization after pickup. Likewise, the ion cluster beam is more intense. The mass spectra show, as well, that ion clusters of the dopants can be produced with only few helium atoms attached, which will be important for messenger spectroscopy. All these findings are important for the scientific research of clusters and nanoscale materials in general.publishersversionpublishe

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure

On Quantum State Observability and Measurement

We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence the dynamics by generating all the unitary evolutions in a Lie group. We investigate to what extent, by an appropriate sequence of evolutions and measurements, we can obtain information on the initial state of the system. We present a system theoretic viewpoint of this problem in that we study the {\it observability} of the system. In this context, we characterize the equivalence classes of indistinguishable states and propose algorithms for state identification

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio