Preferred shapes and modes of internal motion in a system of three identical fermions

The states havingL=0, even parity,S=1/2 or 3/2 of a model system of three identical fermions have beeninvestigated. The pairwise interaction adopted has a repulsive core and an attractive tail. Information on the preferred shapes and on internal motions have been extracted from the wave functions. A comparison is made among the states having symmetric, mixed-symmetric and antisymmetric spatial permutation symmetry. It is found that the symmetry plays an essential role in determining the microscopic structures.     

Symmetry theory in a two-level quantum system

We develop the theory of symmetry for a two-level quantum system in oder to illustrate the main ideas of the general theory of symmetry in quantum theory. It is based on the diffeomorphism of the two-dimensional sphere S ² onto the space of states P ¹ and the isomorphism between the groups P(2) and SO ₃ (). In particular, rotational invariance leads to the appearance of the spin1/2 in a natural way.     

Eigenvalues of the Faddeev equation kernel for a system of three spinless particles

For a system of three spinless particles interacting via separable Yamaguchi potential the possibility of the existence of three-particle resonances is studied. To this end, the eigenvalues _i ^L (E ₃) of the Faddeev equation kernel have been calculated in the c.m.-energy region –30 MeVE ₃15 MeV for total momentum statesL=0 andL=1. It is shown that in the investigated energy range there are no resonances.     

Symmetry properties of a charged fluid in the general theory of relativity

The problem of specifying the symmetry properties of a charged fluid in space-time V₄, which has a definite group of motions, is considered. It is shown that if nonempty spacetime V₄ with an energy-momentum tensor for the charged fluid has symmetry (i.e., admits a group of motions), then the mass density, the pressure, and the four-velocity of the fluid inherits this symmetry, and for an electromagnetic field the relationL f _ij =7.*f _ij is satisfied. The necessary and sufficient conditions are found so that =0 in the case of a one-parameter group. Then additional relationships between and the structure constants are obtained in the case of an r-parameter group. It is shown that under certain conditions the symmetry properties obtained for charged matter are necessary and sufficient conditions for the symmetry of space-time V₄.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 113–117, November, 1978.     

The extended phase space of the BRS approach

The origin of the classical BRS symmetry is discussed for the case of a first class constrained system consisting of a 2n-dimensional phase spaceS with free action of a Lie gauge groupG of dimensionm. The extended phase spaceS _ext of the Fradkin-Vilkovisky approach is identified with a globally trivial vector bundle overS with fibreL*(G)L(G), whereL(G) is the Lie algebra ofG andL*(G) its dual. It is shown that the structure group of the frame bundle of the supermanifoldS _ext is the orthosymplectic group OSp(m,m; 2n), which is the natural invariance group of the super Poisson bracket structure on the function spaceC (S _ext). The action of the BRS operator is analyzed for the caseS=R ²ⁿ with constraints given by pure momenta. The breaking of the osp(m,m; 2n)-invariance down to sp(2n–2m) occurs via an intermediate osp(m; 2n–m). Starting from a (2n+2m)-dimensional system with orthosymplectic invariance, different choices for the BRS operator correspond to choosing different 2n-dimensional constraint supermanifolds inS _ext, which in general characterize different constrained systems. There is a whole family of physically equivalent BRS operators which can be used to describe a particular constrained system.     

Preferred shapes and modes of internal motion in a system of four identical fermions

The 0⁺ and 0^– states of a model fermion system with symmetric and antisymmetric spatial permutation symmetry have been investigated. The pairwise interaction adopted has a repulsive core and an attractive tail. Evidences on the preferred shapes and on modes of internal motions have been extracted from the wave functions. A comparison is made among the states having even or odd parity and being symmetric or antisymmetric. It is found that the symmetry plays an essential role in determining the microscopic structures.Supported by the National Educational Committee of the People's Republic of China     

Stability of 3He2 4He M and 3He3 4He M L = 0,1 Clusters

We have studied the stability of mixed ³He/⁴He clusters in L = 0 and L = 1 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu (TTY) He-He potential. The clusters ³He⁴He_M ( ) and ³He₂⁴He_M (L = 0, S = 0) are stable for M > 1, while to bind two ³He in a triplet state the minimum number of ⁴He is four. Considering clusters with three ³He, ³He₃⁴He₄ is the smallest stable system in the L = 1 state, while ³He₃⁴He₈ is the smallest stable system in the L = 0 state.     

Mössbauer spectroscopy with the 93 keV-resonance in67Zn

The procedures and results of high resolution Mössbauer experiments performed with the 93.3 keV resonance in absorbers of⁶⁷ZnO,⁶⁷ZnS (both wurtzite and sphalerite structures),⁶⁷ZnSe,⁶⁷ZnTe and⁶⁷ZnF₂ are reported. An essentially linear dependence between the isomer shift and the Pauling electronegativity of the ligands was found. A value of r ²=+11×10^–3 fm² is estimated. The Mössbauer parameters for both ZnS structures are equal within present limits of error. In particular, no quadrupole interaction was observed in the wurtzite modification. This indicates a nearly identical local symmetry at the Zn site in the two ZnS structures.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany and the Kernfor-schungszentrum Karlsruhe     

Symmetry breaking and finite-size effects in quantum many-body systems

We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order and the Hubbard model with a (superconducting) off-diagonal long-range order. In the corresponding finite system, the symmetry breaking is usually obscured by quantum fluctuation and one gets a symmetric ground state with a long-range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of orderN ^–1, whereN denotes the number of sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever-increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant timesN ^–1. A crucial feature of the particular low-lying states we consider is that they can be regarded as finite-volume counterparts of the infinite-volume ground states. By forming linear combinations of these low-lying states and the (finite-volume) ground state and by taking infinite-volume limits, we construct infinite-volume ground states with explicit symmetry breaking. We conjecture that these infinite-volume ground states are ergodic, i.e., physically natural. Our general theorems not only shed light on the nature of symmetry breaking in quantum many-body systems, but also provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of interesting examples. The present paper is intended to be accessible to readers without background in mathematical approaches to quantum many-body systems.     

Study of the Influence of the Excitation Laser Power Density on the Intermediate-Field Electric Modulation Component of the GaAs Photoreflection E 0-Signal

The influence of the excitation laser power density L on the amplitude A and characteristic time constant of the intermediate-field electric modulation component of photoreflection spectra measured in the region of the E ₀ fundamental transition of GaAs is studied. Crystalline samples with the charge carrier concentration n 10¹⁶ cm^–3 are investigated for L = 100 W/cm²–1 W/cm². A logarithmic dependence of the electric modulation signal on the excitation laser power density has been established for all examined samples. It is demonstrated that the observed change in the characteristic time constant does not have any noticeable effect on the dependence A(L).     

Modes of internal motion in three-body systems

We propose an approach to investigate the possible internal motions of three-body quantum-mechanical systems held together by pairwise potentials. The method utilizes the shape-density functions which we define and then extract from the eigenwave functions of the system. Through these densities we determine the dominant geometric configurations and modes of internal motion of the 0⁺, 2⁺ and 4⁺ states of a model three-boson system with and without a repulsive core in the interaction.Research supported in part by NSF Grant No. PHY83-06584 and by The Science Fund of the Chinese Academy of Sciences     

Group theory and kink stability equations

Starting from Schrödinger equations withSU(2) group-theoretic potentials, we consider a general family of kinks labeled by two (half-)integers (l, n) with ¦n¦l. A particular choice ofn=0,l=L (L positive integer) leads to a generalL-family, whereL=1 corresponds to sine-Gordon theory, whileL=2 represents the ( ⁴)₁₊₁ model. The ( ⁶)₁₊₁ model can also be recovered withl=3/2,n=–1/2, a particular case of theories labeled byl andn such thatl-n=2 which possess simple kink solutions. We also discuss one-loop order corrections to the kink masses in supersymmetric versions of theL-family. As a byproduct, we obtain the SUSY renormalization of the so-called parameter in sine-Gordon theory.     

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL ^d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq3, with the correlation length of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest are calculated straight-forwardly. In particular, it is shown that forL exceeding a characteristic minimum sizeL _min the forthorder cumulantg _L (T) exhibits a minimum atT _min>T _c, withT _min–T _cL ^–d and the value of the cumulant and the minimum (g(T _min)) behaving asg(T _min)L ^–d. All cumulantsg _L (T) forL approximately intersect at a common crossing pointT _crossL ^–2d, with a universal valueg(T _cross)=1–n/2q, wheren is the order parameter dimensionality. By searching for such a behavior in numerical simulation data, the first order character of a phase transition can be asserted. The usefulness of this approach is shown using data for theq=3,d=3 Potts ferromagnet.     

Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice

A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the lattice. The stiffness exponent governing the scaling of the defect energy E with system size L, (E) ~L ^y, is obtained as y ₃ = 0.25546(3) by reducing the equivalent of lattices up to L = 2¹⁰⁰ in d = 3, and as y ₄ = 0.76382(4) for up to L = 2³⁵ in d = 4. The reduction rules allow the exact determination of the ground state energy, entropy, and also provide an approximation to the overlap distribution. With these methods, some well-know and some new features of diluted hierarchical lattices are calculated.     

Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion and Approach to Equilibrium

We study numerically and theoretically (on a heuristic level) the time evolution of a gas confined to a cube of size L ³ divided into two parts by a piston with mass M _L L ² which can only move in the x-direction. Starting with a uniform double-peaked (non Maxwellian) distribution of the gas and a stationary piston, we find that (a) after an initial quiescent period the system becomes unstable and the piston performs a damped oscillatory motion, and (b) there is a thermalization of the system leading to a Maxwellian distribution of the gas velocities. The time of the onset of the instability appears to grow like L log L while the relaxation time to the Maxwellian grows like L ^7/2.     

Consequences of the complex character of the internal symmetry in supersymmetric theories

The consequences of the invariance of the superpotential under the complexificationG ^c of the internal symmetry group on the determination of the possible patterns of symmetry and supersymmetry breaking are established in a globally supersymmetric theory. In particular, in the case of global internal symmetry we show that a vacuum associaated to a pointz, whereG _z ^c G _z ^c is always degenerate with a vacuum associated to a pointz, whereG _z ^c =G _z ^c ; all the other degeneracies of the minimum of the potential on an orbit ofG ^c are also determined and shown to be completely removed when the internal symmetry is gauged. The zeroes of theD-term of a supersymmetric gauge theory are characterized as the points of the closed orbits ofG ^c which are at minimum distance from the origin; at these pointsG _z ^c =G _z ^c . It is rigorously proved that the minimum of the potential is zero if the gradient of the superpotential vanishes somewhere. It is also shown that theD-term necessarily vanishes at the minimum of the potential if the direction of spontaneous supersymmetry breaking is invariant byG.Partially supported by the Swiss National Science Foundation and INFN, Sezione di PadovaOn leave of absence from the Department of Physics of the University of Padova, Italy     

Geometrical basis for the Standard Model

The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces-the unitary planeC ², the quaternion spaceQ, and the real spaceR ⁴—as well as the real spaceR ³ uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge groupSU(2) _L ×U(1) _Y generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u, d) and (c, s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c ², theb quark at 80 GeV/c ², and thet quark at 2600 GeV/c ².     

Internal symmetries from field theories in higher dimensions

It is suggested that a dynamical space-time symmetry group of a given non-linear relativistic theory is able to generate an internal symmetry group. It is shown that onlyO(2N-1, 1) andO(2N, 1) groups are admitted as simple dynamical symmetry groups, and they implyU(2 ^N –2) as the largest internal symmetry groups. The boson and fermion content of the considered models is determined and a new dynamical symmetry breaking mechanism, different from the spontaneous one, is introduced.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.The author would like to thank Professor J. Niederle for the kind hospitality extended to him during his stay at Bechyn.     

On Bianchi type-I vacuum solutions inR+R 2 theories of gravitation. II. The axially symmetric anisotropic case

The field equations following from a LagrangianL(1/L)(–g)^1/2[(1/2)R+l ²(R _lk R ^lk +R ²)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,+3=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.