Planar Quantum Mechanics: an Intriguing Supersymmetric Example

CERN Document Server

Veneziano, Gabriele

2006-01-01

After setting up a Hamiltonian formulation of planar (matrix) quantum mechanics, we illustrate its effectiveness in a non-trivial supersymmetric example. The numerical and analytical study of two sectors of the model, as a function of 't Hooft's coupling $\\lambda$, reveals both a phase transition at $\\lambda=1$ (disappearence of the mass gap and discontinuous jump in Witten's index) and a new form of strong-weak duality for $\\lambda \\to 1/\\lambda$.

Inverse scattering with supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Baye, Daniel; Sparenberg, Jean-Marc

2004-01-01

The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The use of singular potentials allows adding or removing states from the bound spectrum without contradicting the Levinson theorem. Physical applications of phase-equivalent potentials in nuclear reactions and in three-body systems are described. Derivation of a potential from the phase shift at fixed orbital momentum can also be performed with the supersymmetric inversion by using a Bargmann-type approximation of the scattering matrix or phase shift. A unique singular potential without bound states can be obtained from any phase shift. A limited number of bound states depending on the singularity can then be added. This inversion procedure is illustrated with nucleon-nucleon scattering

Phase holonomy, zero-point energy cancellation and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Iida, Shinji; Kuratsuji, Hiroshi

1987-01-01

We show that the zero-point energy of bosons is cancelled out by the phase holonomy which is induced by the adiabatic deformation of a boson system coupled with a fermion. This mechanism results in a supersymmetric quantum mechanics as a special case and presents a possible dynamical origin of supersymmetry. (orig.)

Formal scattering theory approach to S-matrix relations in supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Amado, R.D.; Cannata, F.; Dedonder, J.P.

1988-01-01

Combining the methods of scattering theory and supersymmetric quantum mechanics we obtain relations between the S matrix and its supersymmetric partner. These relations involve only asymptotic quantities and do not require knowledge of the dynamical details. For example, for coupled channels with no threshold differences the relations involve the asymptotic normalization constant of the bound state removed by supersymmetry

Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Schulze-Halberg, Axel

2017-01-01

A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation. (paper)

Third-order differential ladder operators and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Mateo, J; Negro, J

2008-01-01

Hierarchies of one-dimensional Hamiltonians in quantum mechanics admitting third-order differential ladder operators are studied. Each Hamiltonian has associated three-step Darboux (pseudo)-cycles and Painleve IV equations as a closure condition. The whole hierarchy is generated applying some operations on the cycles. These operations are investigated in the frame of supersymmetric quantum mechanics and mainly involve algebraic manipulations. A consistent geometric representation for the hierarchy and cycles is built that also helps in understanding the operations. Three kinds of hierarchies are distinguished and a realization based on the harmonic oscillator Hamiltonian is supplied, giving an interpretation for the spectral properties of the Hamiltonians of each hierarchy

Supersymmetric quantum mechanics, spinors and the standard model

International Nuclear Information System (INIS)

Woit, P.

1988-01-01

The quantization of the simplest supersymmetric quantum mechanical theory of a free fermion on a riemannian manifold requires the introduction of a complex structure on the tangent space. In 4 dimensions, the subgroup of the group of frame rotations that preserves the complex structure is SU(2) x U(1), and it is argued that this symmetry can be consistently interpreted to be an internal gauge symmetry for the analytically continued theory in Minkowski space. The states of the theory carry the quantum numbers of a generation of leptons in the Weinberg-Salam model. Examination of the geometry of spinors in four dimensions also provides a natural SU(3) symmetry and very simple construction of a multiplet with the standard model quantum numbers. (orig.)

More on homological supersymmetric quantum mechanics

Science.gov (United States)

Behtash, Alireza

2018-03-01

In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantum mechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantum mechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantum mechanics is indicated.

Supersymmetric quantum mechanics, phase equivalence, and low energy scattering anomalies

International Nuclear Information System (INIS)

Amado, R.D.; Cannata, F.; Dedonder, J.P.

1991-01-01

Supersymmetric quantum mechanics links two Hamiltonians with the same scattering (phase equivalence) but different number of bound states. We examine the Green's functions for these Hamiltonians as a prelude to embedding the two-body dynamics in a many-body system. We study the effect of the elimination of a two-body bound state near zero energy for the Efimov effect and Beg's theorem

Twist deformations of the supersymmetric quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Castro, P.G.; Chakraborty, B.; Toppan, F., E-mail: pgcastro@cbpf.b, E-mail: biswajit@bose.res.i, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Kuznetsova, Z., E-mail: zhanna.kuznetsova@ufabc.edu.b [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil)

2009-07-01

The N-extended supersymmetric quantum mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its universal enveloping superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed. (author)

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

International Nuclear Information System (INIS)

Balondo Iyela, Daddy; Govaerts, Jan; Hounkonnou, M. Norbert

2013-01-01

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

Energy Technology Data Exchange (ETDEWEB)

Balondo Iyela, Daddy [International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey–Calavi, 072 B. P. 50 Cotonou, Republic of Benin (Benin); Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain U.C.L., 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Département de Physique, Université de Kinshasa (UNIKIN), B.P. 190 Kinshasa XI, Democratic Republic of Congo (Congo, The Democratic Republic of the); Govaerts, Jan [International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey–Calavi, 072 B. P. 50 Cotonou, Republic of Benin (Benin); Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain U.C.L., 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Hounkonnou, M. Norbert [International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey–Calavi, 072 B. P. 50 Cotonou, Republic of Benin (Benin)

2013-09-15

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.

Determination of excited states of quantum systems by finite difference time domain method (FDTD) with supersymmetric quantum mechanics (SUSY-QM)

Energy Technology Data Exchange (ETDEWEB)

Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id [Physics Study Program, University of Mataram, Jln. Majapahit 62 Mataram, NTB (Indonesia)

2016-04-19

We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

Ground State Structure of a Coupled 2-Fermion System in Supersymmetric Quantum Mechanics

Science.gov (United States)

Finster, Felix

1997-05-01

We prove the uniqueness of the ground state for a supersymmetric quantum mechanical system of two fermions and two bosons, which is closely related to theN=1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like

Recent developments in the N-extended supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Toppan, Francesco

2007-01-01

In this paper we review some recent developments in the understanding of the supersymmetric quantum mechanics for large-N values of the extended supersymmetries. A list of the topics here covered includes the new available classification of the finite linear irreducible representations, the construction of manifestly off-shell invariant actions without introducing a superfield formalism, the notion of the 'fusion algebra' of the irreducible representations, the connection (for N = 8) with the octonionic structure constants, etc. The results presented are based on the work of the author and his collaborators. (author)

Supersymmetric quantum mechanics for string-bits

International Nuclear Information System (INIS)

Thorn, C.B.

1997-01-01

The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 7, 10 space-time dimensions. These are the cases for which classical superstring makes sense, and also the values of d for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question they address is: when is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. They show that the answer is affirmative for d = 1,2, negative for d = 8, and so far inconclusive for d = 4

Deformed supersymmetric quantum mechanics with spin variables

Science.gov (United States)

Fedoruk, Sergey; Ivanov, Evgeny; Sidorov, Stepan

2018-01-01

We quantize the one-particle model of the SU(2|1) supersymmetric multiparticle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter m and SU(2) spin q\\in (Z_{>0,}1/2+Z_{≥0}) . It is found that the states at the fixed energy level form irreducible multiplets of the supergroup SU(2|1). Also, the hidden superconformal symmetry OSp(4|2) of the model is revealed in the classical and quantum cases. We calculate the OSp(4|2) Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed q are unified into an irreducible OSp(4|2) multiplet.

Planarizable Supersymmetric Quantum Toboggans

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2011-01-01

Roč. 7, - (2011), 018/1-018/23 ISSN 1815-0659. [Workshop on Supersymmetric Quantum Mechanics and Spectral Design. Benasque, 18.07.2010-30.07. 2010] R&D Projects: GA ČR GAP203/11/1433 Institutional research plan: CEZ:AV0Z10480505 Keywords : supersymmetry * Schrodinger equation * complexified coordinates Subject RIV: BE - Theoretical Physics Impact factor: 1.071, year: 2011

Supersymmetric quantum mechanics for string bits

International Nuclear Information System (INIS)

Thorn, C.B.

1997-01-01

We develop possible versions of supersymmetric single-particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions d=1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 6, and 10 space-time dimensions. These are the cases for which open-quotes classicalclose quotes superstring makes sense, and also the values of d for which Hooke close-quote s force law is compatible with the simplest superparticle dynamics. The basic question we address is the following: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for d=1,2, negative for d=8, and so far inconclusive for d=4. copyright 1997 The American Physical Society

Ground state structure of a coupled 2-fermion system in supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Finster, F.

1997-01-01

We prove the uniqueness of the ground state for a supersymmetric quantum mechanical system of two fermions and two bosons, which is closely related to the N=1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like. copyright 1997 Academic Press, Inc

Self-isospectral periodic potentials and supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Dunne, G.; Feinberg, J.

1998-01-01

We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast with the standard nonperiodic case where either one or neither (but not both) of the isospectral pair has a zero mode. Thus it is possible to have supersymmetry unbroken and yet also have a vanishing Witten index. We present some explicit exactly soluble examples for which the isospectral potentials have identical band spectra, and which are open-quotes self-isospectralclose quotes in the sense that the potentials have identical shape, but are translated by one half-period relative to one another. copyright 1997 The American Physical Society

Supersymmetry and quantum mechanics

International Nuclear Information System (INIS)

Cooper, F.; Sukhatme, U.

1995-01-01

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p. ((orig.))

On the irreps of the N-extended supersymmetric quantum mechanics and their fusion graphs

International Nuclear Information System (INIS)

Toppan, Francesco.

2006-12-01

In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D N-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The N = 2 graphs are here explicitly presented for the first time. (author)

Supersymmetric hadronic mechanics and procedures for isosupersymmetrization

International Nuclear Information System (INIS)

Ntibashirakandi, L.; Callebaut, D.K.

1994-01-01

In this paper the authors present the Lie-Santilli lifting of Witten's one-dimensional supersymmetric quantum mechanical model within the context of supersymmetric hadronic mechanics and extended it to three dimensions. They show that the model describes the motion of a spin one-half particle in a central isosuperpotential. Choosing this isosuperpotential within the specific isosupersymmetrization procedure, their theory produces the model of hadronic harmonic oscillator plus isotopic spin-orbit couplings. They finally indicate that their model describes a particle under conventional potentials plus nonlocal-nonhamiltonian corrections expected in deep penetrations of the wavepackets. As such, the model appears to be significant for the recently proposed chemical synthesis of unstable hadrons via lighter hadrons, which is prohibited by quantum mechanics, but permitted by the covering hadronic mechanics. 16 refs

Local rings of singularities and N=2 supersymmetric quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Klimek, S.; Lesniewski, A. (Harvard Univ., Cambridge, MA (USA))

1991-02-01

We investigate the Kaehler structure arising in n-component, N = 2 supersymmetric quantum mechanics. We define L{sup 2}-cohomology groups of a modified {delta}-operator and relate them to the corresponding spaces of harmonic forms. We prove that the cohomology is concentrated in the middle dimension, and is isomorphic to the direct sum of the local rings of the singularities of the superpotential. In the physics language, this means that the number of ground states is equal to the absolute value of the index of the supercharge, and each ground state contains exactly n fermions. (orig.).

Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems

Science.gov (United States)

Fedoruk, Sergey; Ivanov, Evgeny; Lechtenfeld, Olaf; Sidorov, Stepan

2018-04-01

SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an N=4 supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra \\widehat{su}(2\\Big|1) . The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.

The supercharge and superconformal symmetry for N=1 supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Clark, T.E.; Love, S.T.; Nowling, S.R.

2002-01-01

The superspace Lagrangian formulation of N=1 supersymmetric quantum mechanics is presented. The general Lagrangian constructed out of chiral and antichiral supercoordinates containing up to two derivatives and with a canonically normalized kinetic energy term describes the motion of a nonrelativistic spin 1/2 particle with Lande g-factor 2 moving in two spatial dimensions under the influence of a static but spatially dependent magnetic field. Noether's theorem is derived for the general case and is used to construct superspace dependent charges whose lowest components give the superconformal generators. The supercoordinates of charges containing an R symmetry charge, the supersymmetry charges and the Hamiltonian are combined to form a supercharge supercoordinate. Superconformal Ward identities for the quantum effective action are derived from the conservation equations and the source of potential symmetry breaking terms are identified

Supersymmetric quantum corrections and Poisson-Lie T-duality

International Nuclear Information System (INIS)

Assaoui, F.; Lhallabi, T.; Abdus Salam International Centre for Theoretical Physics, Trieste

2000-07-01

The quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric nonlinear sigma model in the sense of Poisson-Lie T-duality. (author)

Supersymmetric mechanics

International Nuclear Information System (INIS)

Stelle, Kellogg S

2007-01-01

With the development of the electronic archives in high-energy physics, there has been increasing questioning of the role of traditional publishing styles, particularly in the production of conference books. One aspect of traditional publishing that still receives wide appreciation, however, is in the production of well-focussed pedagogical material. The present two-volume edition, 'Supersymmetric Mechanics-Vol 1', edited by S Bellucci and 'Supersymmetric Mechanics-Vol 2', edited by S Bellucci, S Ferrara and A Marrani, is a good example of the kind of well-digested presentation that should still find its way into university libraries. This two-volume set presents the material of a set of pedagogical lectures presented at the INFN National Laboratory in Frascati over a two-year period on the subject of supersymmetric mechanics. The articles include the results of discussions with the attending students after the lectures. Overall, this makes for a useful compilation of material on a subject that underlies much of the current effort in supersymmetric approaches to cosmology and the unification programme. The first volume comprises articles on 'A journey through garden algebras' by S Bellucci, S J Gates Jr and E Orazi on linear supermultiplet realizations in supersymmetric mechanics,'Supersymmetric mechanics in superspace' by S Bellucci and S Krivonos, 'Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes' by V P Nair, 'Elements of (super) Hamiltonian formalism' by A Nersessian and 'Matrix mechanics' by C Sochichiu. The second volume consists entirely of a masterful presentation on 'The attractor mechanism and space time singularities' by S Ferrara. This presents a comprehensive and detailed overview of the structure of supersymmetric black hole solutions in supergravity, critical point structure in the scalar field moduli space and the thermodynamic consequences. This second volume alone makes the set a worthwhile addition to the research

Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: xbataxel@gmail.com; Rivas, Jesus Morales [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jmr@correo.azc.uam.mx; Pena Gil, Jose Juan [Universidad Autonoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atomica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 Mexico D.F. (Mexico)], E-mail: jjpg@correo.azc.uam.mx; Garcia-Ravelo, Jesus [Escuela Superior de Fisica y Matematicas, IPN, Unidad Profesional Adolfo Lopez Mateos, Col. San Pedro Zacatenco, Edificio 9, 07738 Mexico D.F. (Mexico)], E-mail: ravelo@esfm.ipn.mx; Roy, Pinaki [Physics and Applied Mathematics Unit, Indian Statistical Institute, Calcutta-700108 (India)], E-mail: pinaki@isical.ac.in

2009-04-20

We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

Exact solutions of the Fokker-Planck equation from an nth order supersymmetric quantum mechanics approach

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Rivas, Jesus Morales; Pena Gil, Jose Juan; Garcia-Ravelo, Jesus; Roy, Pinaki

2009-01-01

We generalize the formalism of nth order Supersymmetric Quantum Mechanics (n-SUSY) to the Fokker-Planck equation for constant diffusion coefficient and stationary drift potential. The SUSY partner drift potentials and the corresponding solutions of the Fokker-Planck equation are given explicitly. As an application, we generate new solutions of the Fokker-Planck equation by means of our first- and second-order transformation.

Supersymmetric quantum mechanics and the index theorem for arbitrary Lorentz irreps

Energy Technology Data Exchange (ETDEWEB)

Jarvis, P.D.; Twisk, S.

1987-05-01

A new formalism is presented for the derivation of index theorems from the supersymmetric quantum mechanics of the Dirac operator, based on a discrete approximation to the path integral. Operator ordering in H (i..gamma..sup(..mu..)Dsub(..mu..))/sup 2/ dictates the form of the action, and the N ..-->.. infinity limit yields the correct form of the index theorem for the U(1) anomaly. It is established that internal degrees of freedom may be represented by fermions and/or bosons. In the purely gravitational case, the bosonic formulation yields a generating function for the contribution to the anomaly for spinor fields carrying arbitrary irreps (1/2A,1/2B) of the local SO(4) group.

Supersymmetric quantum mechanics and the index theorem for arbitrary Lorentz irreps

International Nuclear Information System (INIS)

Jarvis, P.D.; Twisk, S.

1987-01-01

A new formalism is presented for the derivation of index theorems from the supersymmetric quantum mechanics of the Dirac operator, based on a discrete approximation to the path integral. Operator ordering in H (iγsup(μ)Dsub(μ)) 2 dictates the form of the action, and the N → infinity limit yields the correct form of the index theorem for the U(1) anomaly. It is established that internal degrees of freedom may be represented by fermions and/or bosons. In the purely gravitational case, the bosonic formulation yields a generating function for the contribution to the anomaly for spinor fields carrying arbitrary irreps (1/2A,1/2B) of the local SO(4) group. (author)

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Institute of Scientific and Technical Information of China (English)

Tang Wen-Lin; Tian Gui-Hua

2011-01-01

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Resonances in A=6 nuclei: use of supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Dutta, S.K.; Das, T.K.; Khan, M.A.; Chakrabarti, B.

2004-01-01

We propose a novel theoretical technique for the calculation of resonances at low excitation energies in weakly bound systems. Starting from an effective potential, supersymmetric quantum mechanics can be successfully used to generate families of isospectral potentials having desirable and adjustable properties. For resonance states, for which there is no bound ground state of the same spin-parity, one can construct an isospectral potential with a bound state in the continuum (BIC). The potential looks quite different but is strictly isospectral with the original one. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family facilitating an easier and more accurate calculation of the resonance energy. Application to 6 He, 6 Be, and 6 Li systems yields quite accurate results. The beauty of our technique: We get both the bound ground state and the resonances by a single technique and using the same potential. (author)

1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)

1980-01-01

The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived

Supersymmetric many-particle quantum systems with inverse-square interactions

International Nuclear Information System (INIS)

Ghosh, Pijush K

2012-01-01

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to the exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-Hermitian supersymmetric quantum systems with a special emphasis on the rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigenfunctions and eigenvalues. The Calogero–Marchioro model with dynamical SU(1, 1|2) supersymmetry and a quantum system related to the short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized. (topical review)

Dynamical parasupersymmetries in quantum mechanics

International Nuclear Information System (INIS)

Durand, S.; Vinet, L.

1990-01-01

This paper reports on supersymmetric field theories that have the distinctive feature of being invariant under transformations that mix bosonic and fermionic variables. Reduction to 0 + 1 dimensions yields mechanical models with an analogous invariance. In this case, the Grassmannian variables are interpreted as describing (classically) the spin degrees of freedom of the particles involved. After canonical quantization, the corresponding quantities obey the standard anticommutation relations of fermionic creation and annihilation operators. It is known that paraquantitization offers alternative to the usual quantization scheme. In this framework, one can expect that it is possible to construct parasupersymmetric theories, that is, theories which are invariant under transformations between bosonic and parafermionic variables. As a matter of fact, Rubakov and Spiridonov has recently shown how the parasupersymmetric generalization of supersymmetric Quantum Mechanics proceeds. In this case, the fermionic creation and annihilation operators obey paracommutation relations. The applications of supersymmetric Quantum Mechanics are many. One might hope that its parasupersymmetric generalization will be as useful. The elaboration of parasupersymmeric Quantum Mechanics moreover has led to new mathematical constructs; indeed, the symmetry generators realize algebras involving products of degree higher than 2

Localized fermions on domain walls and extended supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Oikonomou, V K

2014-01-01

We study fermionic fields localized on topologically unstable domain walls bounded by strings in a grand unified theory theoretical framework. Particularly, we found that the localized fermionic degrees of freedom, which are up and down-quarks as well as charged leptons, are connected to three independent N = 2, d = 1 supersymmetric quantum mechanics algebras. As we demonstrate, these algebras can be combined to form higher order representations of N = 2, d = 1 supersymmetry. Due to the uniform coupling of the domain wall solutions to the down-quarks and leptons, we also show that a higher order N = 2, d = 1 representation of the down-quark–lepton system is invariant under a duality transformation between the couplings. In addition, the two N = 2, d = 1 supersymmetries of the down-quark–lepton system, combine at the coupling unification scale to form an N = 4, d = 1 supersymmetry. Furthermore, we present the various extra geometric and algebraic attributes that the fermionic systems acquire, owing to the underlying N = 2, d = 1 algebras. (paper)

Supersymmetric quantum mechanics approach to a nonlinear lattice

International Nuclear Information System (INIS)

Ricotta, Regina Maria; Drigo Filho, Elso

2011-01-01

Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)

On q-deformed supersymmetric classical mechanical models

International Nuclear Information System (INIS)

Colatto, L.P.; Matheus Valle, J.L.

1995-10-01

Based on the idea of quantum groups and paragrassmann variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp 2πi/k dealing with the k=3 case. The coordinates of the q-superspace are a commuting parameter t and a paragrassmann variable θ, where θ 3 =0. The generator and covariant derivative are obtained, as well as the action for some possible superfields. (author). 13 refs

Supersymmetry in quantum mechanics

CERN Document Server

Cooper, Fred; Sukhatme, Uday

2001-01-01

This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by

Supersymmetry in quantum mechanics

International Nuclear Information System (INIS)

Lahiri, A.; Roy, P.K.; Bagghi, B.

1990-01-01

A pedagogical review on supersymmetry in quantum mechanics is presented which provides a comprehensive coverage of the subject. First, the key ingredients of the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltonian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. The authors also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N = 1 and N = 2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. They treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called 'shape-invariance' of potentials. To make transparent the relationship between supersymmetry and solvable potentials, they also solve several examples. They then go over the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. They show that the ladder operator technique may be suitable modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying he definition of Witten's index. Finally, the authors perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases

Bound states in the continuum generated by supersymmetric quantum mechanics and phase rigidity of the corresponding wavefunctions

International Nuclear Information System (INIS)

Demić, Aleksandar; Milanović, Vitomir; Radovanović, Jelena

2015-01-01

Supersymmetric quantum mechanics (SUSYQM) is a method that can be used for generating complex potentials with entirely real spectrum with bound states in the continuum (BIC). These complex potentials are isospectral with the initial one, but SUSYQM method adds discrete BIC's at selected energies. Corresponding wavefunctions created by SUSYQM are biorthogonal and complex, hence we can discuss their phase rigidity and illustrate the application of SUSYQM on the examples of three specific potential profiles (free electron, negative Dirac potential and quantum well with infinite walls). - Highlights: • We present SUSYQM method for generating complex potentials with entirely real spectrum. • Phase rigidity and normalizability of wavefunctions in complex potential is discussed. • Numerical application is performed on three specific potential profiles.

Supersymmetric quantum mechanics under point singularities

International Nuclear Information System (INIS)

Uchino, Takashi; Tsutsui, Izumi

2003-01-01

We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

Quantum conserved charges in N=1 and N=2 supersymmetric sine-Gordon theories

International Nuclear Information System (INIS)

Kobayashi, Ken-ichiro; Uematsu, Tsuneo; Yu Yangzheng

1993-01-01

We investigate quantum conservation laws in the N=1 and N=2 supersymmetric sine-Gordon theories. We study conserved charges at the quantum level based on perturbation theory formulated in superspace. It will turn out that there exist extra conserved charges of the vertex operator type at the quantum level and they generate a quantum group symmetry in supersymmetric sine-Gordon systems. We also discuss the implication of the quantum group symmetry on the S-matrix structure. (orig.)

How to quantize supersymmetric theories

International Nuclear Information System (INIS)

Smilga, A.V.

1985-01-01

A recipe for resolving the ordering ambiguities in quantum hamiltonians of supersymmetric theories is suggested. The Weyl ordering procedure applied to classical supercharges expressed as functions on the phase space of a classically supersymmetric system is shown to result in quantum operators which satisfy usual SUSY algebra. The quantum hamiltonian does not always coincide with the Weyl ordered classical hamiltonian function. The difference is due to that the Weyl symbol of the supercharge anticommutator does not coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The procedure is applied to supersymmetric σ-models (both N=2 and N=1 cases are analyzed) and also to the supersymmetric SU(2) Yang-Mills theory. Only quantum mechanical systems following from field theories when fields are assumed to be independent of space coordinates are considered. For gauge theories thesuggested recipe for quantization leads to the same result as the well-known Dirac recipe

Quantum cosmology. The supersymmetric perspective. Vol. 1. Fundamentals

International Nuclear Information System (INIS)

Vargas Moniz, Paulo

2010-01-01

The two volumes that comprise Quantum Cosmology tackle the quantum description of the early universe from the perspective of supersymmetric models of elementary particle physics. The first volume is an accessible primer that covers the basics of the field, critically discussing ideas and concepts that comprise our current knowledge of supersymmetry and supergravity. After reviewing the fundamentals, it provides a thorough analysis of a first set of quantum cosmological models. The second volume is dedicated to more advanced topics. In it, the scope for analyzing quantum cosmological models within a supersymmetric framework is broadened. As much as possible, these two volumes treat what we know, what we think we know and what we think we do not know on an equal footing. Complete with problems and solutions for each chapter, the books are ideal for young, inquisitive minds eager to embark on in-depth research in this field. They provide readers with the tools they need to go on their own, pushing them to ask the right questions rather than seek definitive answers. (orig.)

Supersymmetric quantum spin chains and classical integrable systems

International Nuclear Information System (INIS)

Tsuboi, Zengo; Zabrodin, Anton; Zotov, Andrei

2015-01-01

For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.

Instantons in supersymmetric theories

International Nuclear Information System (INIS)

Novikov, V.A.; Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I.

1982-01-01

Instanton effects are considered for a sample of supersymmetric theories: quantum mechanics, gluodynamics. Higgs model. The problem is how to reconcile the apparent lack of the boson-fermion symmetry in the effective instanton induced interaction with supersymmetry of the corresponding lagrangians. It is shown that in case of quantum mechanics and Higgs model there is no conflict between supersymmetry and the instanton calculus since the Ward identities, associated with the supersymmetry transformations, are satisfied. In case of supersymmetric gluodynamics the standard instanton calculus explicity violates the Ward identities. This is due to the lack of symmetry in the standard class of classical solutions used in the instanton calculus

PREFACE: Progress in supersymmetric quantum mechanics

Science.gov (United States)

Aref'eva, I.; Fernández, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.

2004-10-01

The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models

Supersymmetric quantum mechanics of the flux tube

Science.gov (United States)

Belitsky, A. V.

2016-12-01

The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl (2 | 1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their factorized form. The discussion corresponds to leading order of perturbation theory.

A simple method for generating exactly solvable quantum mechanical potentials

CERN Document Server

Williams, B W

1993-01-01

A simple transformation method permitting the generation of exactly solvable quantum mechanical potentials from special functions solving second-order differential equations is reviewed. This method is applied to Gegenbauer polynomials to generate an attractive radial potential. The relationship of this method to the determination of supersymmetric quantum mechanical superpotentials is discussed, and the superpotential for the radial potential is also derived. (author)

Chaos and random matrices in supersymmetric SYK

Science.gov (United States)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

The quantum mechanics of the supersymmetric nonlinear sigma-model

International Nuclear Information System (INIS)

Davis, A.C.; Macfarlane, A.J.; Popat, P.C.; Holten, J.W. van

1984-01-01

The classical and quantum mechanical formalisms of the models are developed. The quantisation is done in such a way that the quantum theory can be represented explicitly in as simple a form as possible, and the problem of ordering of operators is resolved so as to maintain the supersymmetry algebra of the classical theory. (author)

Supersymmetric gauge field theories

International Nuclear Information System (INIS)

Slavnov, A.A.

1976-01-01

The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models

Deformed supersymmetric mechanics

International Nuclear Information System (INIS)

Ivanov, E.; Sidorov, S.

2013-01-01

Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N = 4, d = 1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a deformation of the standard N = 4, d = 1 supersymmetry by a mass parameter m. As instructive examples we consider at the classical and quantum levels the models associated with the supermultiplets (1,4,3) and (2,4,2) and find out interesting interrelations with some previous works on nonstandard d = 1 supersymmetry. In particular, the d = 1 systems with 'weak supersymmetry' are naturally reproduced within our SU(2|1) superfield approach as a subclass of the (1,4,3) models. A generalization to the N = 8, d = 1 case implies the supergroup SU(2|2) as a candidate deformed worldline supersymmetry

A new perturbative approximation applied to supersymmetric quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.

1988-01-01

We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

The interplay of supersymmetry and ΡΤ symmetry in quantum mechanics

International Nuclear Information System (INIS)

Levai, G.; Znojil, M.

2003-01-01

The unusual features of ΡΤ symmetric potentials naturally raise the question how this symmetry is related to other symmetry concepts characterizing quantum mechanical potentials. One particularly interesting aspect of this question stems from the fact that ΡΤ symmetric potentials have two sets of normalizable solutions distinguished by the q ±1 quasi-parity quantum number. This also means that there are two nodeless normalizable in these potentials, and thus it is possible to define two superpotentials in the supersymmetric quantum mechanical formalism. (R.P.)

Supersymmetric classical mechanics: free case

Energy Technology Data Exchange (ETDEWEB)

Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza]. E-mail: rafael@cfp.ufpb.br; Almeida, W. Pires de [Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza; Fonseca Neto, I. [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica

2001-06-01

We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, {phi}(t;{theta}). (author)

Ultraviolet divergences in non-renormalizable supersymmetric theories

International Nuclear Information System (INIS)

Smilga, A.

2017-01-01

We present a pedagogical review of our current understanding of the ultraviolet structure of N =(1, 1) 6D supersymmetric Yang-Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higher-dimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially of extended supersymmetric theories) is that these counterterms may not be invariant off-shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on-shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behavior.

Extended SUSY quantum mechanics, intertwining operators and coherent states

International Nuclear Information System (INIS)

Bagarello, F.

2008-01-01

We propose an extension of supersymmetric quantum mechanics which produces a family of isospectral Hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given. Further, we show how to build up vector coherent states of the Gazeau-Klauder type associated to our Hamiltonians

Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetry

International Nuclear Information System (INIS)

Hibberd, Katrina; Roditi, Itzhak; Links, Jon; Foerster, Angela

1999-11-01

The nested algebraic Bethe Ansatz is presented for the anisotropic supersymmetric U model maintaining quantum a supersymmetry. The Bethe Ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given. (author)

Quantum integrability and supersymmetric vacua

International Nuclear Information System (INIS)

Nekrasov, Nikita; Shatashvili, Samson

2009-01-01

Supersymmetric vacua of two dimensional N=4 gauge theories with matter, softly broken by the twisted masses down to N=2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2) XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T 2 . A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as T * Gr(N,L) and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. These more general spin chains correspond to quiver gauge theories with twisted masses, with classical gauge groups. We give the gauge-theoretic interpretation of Drinfeld polynomials and Baxter operators. In the classical weak coupling limit our results make contact with Nakajima constructions. Toric compactifications of four dimensional N=2 theories lead to the instanton corrected Bethe equations. (author)

CPT-conserving hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

Czech Academy of Sciences Publication Activity Database

Bagchi, B.; Quesne, C.; Znojil, Miloslav; Banerjee, A.; Geyer, HB; Caliceti, E.; Cannata, F.

2005-01-01

Roč. 20, č. 30 (2005), s. 7107-7128 ISSN 0217-751X R&D Projects: GA AV ČR IAA1048302 Institutional research plan: CEZ:AV0Z10480505 Keywords : PT-symmetric Hamiltonians * CPT-symmetric quantum-mechanics * supersymmetric quantum mechanics Subject RIV: BE - Theoretical Physics Impact factor: 1.472, year: 2005

Low energy dynamics of monopoles in supersymmetric Yang-Mills theories with hypermultiplets

International Nuclear Information System (INIS)

Kim, Chanju

2006-01-01

We derive the low energy dynamics of monopoles and dyons in N = 2 supersymmetric Yang-Mills theories with hypermultiplets in arbitrary representations by utilizing a collective coordinate expansion. We consider the most general case that Higgs fields both in the vector multiplet and in the hypermultiplets have nonzero vacuum expectation values. The resulting theory is a supersymmetric quantum mechanics which has been obtained by a nontrivial dimensional reduction of two-dimensional (4,0) supersymmetric sigma models with potentials

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

International Nuclear Information System (INIS)

Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

2006-01-01

We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out

Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

Science.gov (United States)

Polotto, Franciele; Drigo Filho, Elso; Chahine, Jorge; Oliveira, Ronaldo Junio de

2018-03-01

This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker-Planck equation is mapped onto a Schrödinger-type equation due to the well-known solutions of the latter. Through a semi-analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein Tm CSP was simulated at a Cα level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of Tm CSP having the well-known 'U' shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems.

Supersymmetric mechanics. Vol. 2. The attractor mechanism and space time singularities

International Nuclear Information System (INIS)

Bellucci, S.; Marrani, A.; Ferrara, S.

2006-01-01

This is the second volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. The first volume appears as Lect. Notes Physics, Vol. 698 ''Supersymmetric Mechanics, Vol.1: Supersymmetry, Noncommutativity and Matrix Models'' (2006) ISBN: 3-540-33313-4. The present extensive lecture supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. In such a framework, supersymmetry seems to be related to dynamical systems with fixed points, describing the equilibrium state and the stability features of the thermodynamics of black holes. After a qualitative overview, explicit examples realizing the attractor mechanism are treated at some length; they include relevant cases of asymptotically flat, maximal and non-maximal, extended supergravities in 4 and 5 dimensions. A number of recent advances along various directions of research on the attractor mechanism are also given. (orig.)

Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations

CERN Document Server

Riotto, Antonio

1998-01-01

The closed time-path (CPT) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CPT formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort t...

On quantization of supersymmetric theories

International Nuclear Information System (INIS)

Smilga, A.V.

1985-01-01

A recipe to resolve ordering ambiguities in the quantum hamiltonian of supersymmetric theories is suggested. The Weyl ordering prescription for supercharge operators should be employed to preserve SUSY algebra on the quantum level. The quantum hamiltonian does not generally coincide with the Weyl ordered classical hamiltonian, the difference being due to the fact that the Weyl symbol of anticommutator of supercharges does not generally coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The suggested procedure is applied in the examples of N=1 and N=2 supersymmetric σ-models analyzed in the constant field limit

Supersymmetric construction of exactly solvable potentials and nonlinear algebras

International Nuclear Information System (INIS)

Junker, G.; Roy, P.

1998-01-01

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found that these ladder operators together with the Hamilton operator form a nonlinear algebra which is of quadratic and cubic type for the SUSY partners of the linear and radial harmonic oscillator

Electroweak breaking in supersymmetric models

CERN Document Server

Ibáñez, L E

1992-01-01

We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)

Second Hopf map and supersymmetric mechanics with Yang monopole

International Nuclear Information System (INIS)

Gonzales, M.; Toppan, F.; Kuznetsova, Z.; Nersessian, F.; Yeghikyan, V.

2009-01-01

We propose to use the second Hopf map for the reduction (via SU(2) group action) of the eight-dimensional supersymmetric mechanics to five-dimensional supersymmetric systems specified by the presence of an SU(2) Yang monopole. For our purpose we develop the relevant Lagrangian reduction procedure. The reduced system is characterized by its invariance under the N = 5 or N = 4 supersymmetry generators (with or without an additional conserved BRST charge operator) which commute with the su(2) generators. (author)

4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

International Nuclear Information System (INIS)

Han, Muxin

2016-01-01

A class of 3d N=2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction http://dx.doi.org/10.1007/s00220-013-1863-2 in 3d-3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in http://dx.doi.org/10.1007/JHEP12(2014)177 from the 3d N=2 gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

Quasicomplex N=2, d=1 Supersymmetric Sigma Models

Directory of Open Access Journals (Sweden)

Evgeny A. Ivanov

2013-11-01

Full Text Available We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1 multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0 and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry.

The particle interpretation of N = 1 supersymmetric spin foams

Energy Technology Data Exchange (ETDEWEB)

Baccetti, Valentina [Dipartimento di Fisica ' E. Amaldi' , Universita degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma (Italy); Livine, Etera R [Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d' Italie, 69007 Lyon (France); Ryan, James P, E-mail: baccetti@neve.fis.uniroma3.i, E-mail: etera.livine@ens-lyon.f, E-mail: james.ryan@aei.mpg.d [MPI fuer Gravitationsphysik, Albert Einstein Institute, Am Muehlenberg 1, D-14476 Potsdam (Germany)

2010-11-21

We show that N = 1-supersymmetric BF theory in 3D leads to a supersymmetric spin foam amplitude via a lattice discretization. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3D gravity coupled to embedded fermionic Feynman diagrams.

The particle interpretation of N = 1 supersymmetric spin foams

International Nuclear Information System (INIS)

Baccetti, Valentina; Livine, Etera R; Ryan, James P

2010-01-01

We show that N = 1-supersymmetric BF theory in 3D leads to a supersymmetric spin foam amplitude via a lattice discretization. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3D gravity coupled to embedded fermionic Feynman diagrams.

Quantum-mechanical scattering in one dimension

International Nuclear Information System (INIS)

Boya, Luis J.

2008-01-01

The purpose of this mainly pedagogical review is to fill a lacuna in the usual treatment of scattering in quantum mechanics, by showing the essential of it in the simplest, one-dimensional setting. We define in this situation amplitudes and scattering coefficients and deal with optical and Levinson' theorems as consequences of unitarity in coordinate or momentum space. Parity waves en lieu of partial waves, integral equations and Born series, etc., are defined naturally in this frame. Several solvable examples are shown. Two topics best studied in 1d are transparent potentials and supersymmetric quantum mechanics. Elementary analytical properties and general behaviour of amplitudes give rise to study inverse problems, that is, recovering the potential from scattering data. Isospectral deformations of the wave equation give relations with some nonlinear evolution equations (Lax), solvable by the inverse scattering method (Kruskal), and we consider the KdV equation as an example. We also refer briefly to some singular potentials, where, e.g., the essence of renormalization can be read off again in the simplest setting. The whole paper emphasizes the tutorial and introductory aspects

On the supersymmetric solitons and monopoles

International Nuclear Information System (INIS)

Hruby, J.

1978-01-01

The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is mass of the soliton without the quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension

SUSY anomaly in quantum-mechanical systems

International Nuclear Information System (INIS)

Smilga, A.V.

1987-01-01

Explicit examples of supersymmetric systems involving finite numbers of degrees of freedom where quantum supersymmetry algebra cannot be preserved on the classical level, are constructed. Resolving the ordering ambiguities in different ways leads either to a modified algebra or to a reduced algebra, or totally destroys supersymmetry

Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics

International Nuclear Information System (INIS)

Kuznetsova, Zhanna; Rojas, Moises; Toppan, Francesco

2006-01-01

We present an algorithmic classification of the irreps of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields. Our work is based on the 1-to-1 correspondence between Weyl-type Clifford algebras (whose irreps are fully classified) and classes of irreps of the N-extended 1D supersymmetry. The complete classification of irreps is presented up to N ≤ 10. The fields of an irrep are accommodated in l different spin states. N = 10 is the minimal value admitting length l>4 irreps. The classification of length-4 irreps of the N = 12 and real N = 11 extended supersymmetries is also explicitly presented. Tensoring irreps allows us to systematically construct manifestly (N-extended) supersymmetric multi-linear invariants without introducing a superspace formalism. Multi-linear invariants can be constructed both for unconstrained and multi-linearly constrained fields. A whole class of off-shell invariant actions are produced in association with each irreducible representation. The explicit example of the N = 8 off-shell action of the (1,8,7) multiplet is presented. Tensoring zero-energy irreps leads us to the notion of the fusion algebra of the 1D N-extended supersymmetric vacua

New dualities of supersymmetric gauge theories

CERN Document Server

2016-01-01

This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...

Dynamical symmetry as a tool to understanding properties of supersymmetric partner potentials. Example of so(2,1) symmetry

International Nuclear Information System (INIS)

Wehrhahn, R.F.; Cooper, I.L.

1992-05-01

Analysis of the dynamical symmetry of a system is used to predict properties arising from its supersymmetric quantum mechanical treatment. Two applications of the so(2,1) algebra, the Coulomb potential and Morse oscillator potential which display different structure with respect to the dynamical symmetry, are studied. This difference is shown to be responsible for the behaviour of the respective supersymmetric partner potentials. (orig.)

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Teschner, J.; Vartanov, G.S.

2012-02-15

We revisit the definition of the 6j-symbols from the modular double of U{sub q}(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

International Nuclear Information System (INIS)

Teschner, J.; Vartanov, G.S.

2012-02-01

We revisit the definition of the 6j-symbols from the modular double of U q (sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)

Supersymmetrical dual string theories and their field theory limits: A review

International Nuclear Information System (INIS)

Green, M.B.

1985-01-01

This paper outlines the construction and properties of supersymmetric string theories. Such theories, which describe the quantum mechanics of relativistic strings in ten-space time dimensions contain both N=4 Yang-Mills and N=8 supergravity field theories as special limits in which the string tension becomes infinite. Calculations of one-loop S-matrix elements reveal remarkable finiteness properties

The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation.

Science.gov (United States)

Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G

2009-07-02

We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.

N =4 supersymmetric mechanics on curved spaces

Science.gov (United States)

Kozyrev, Nikolay; Krivonos, Sergey; Lechtenfeld, Olaf; Nersessian, Armen; Sutulin, Anton

2018-04-01

We present N =4 supersymmetric mechanics on n -dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten-Dijkgraaf-Verlinde-Verlinde equations specified by the presence of the manifold's curvature tensor. Solutions of original Witten-Dijkgraaf-Verlinde-Verlinde equations and related prepotentials defining N =4 superconformal mechanics in flat space can be lifted to s o (n )-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of n copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.

Small numbers in supersymmetric theories of nature

International Nuclear Information System (INIS)

Graesser, Michael L.

1999-01-01

The Standard Model of particle interactions is a successful theory for describing the interactions of quarks, leptons and gauge bosons at microscopic distance scales. Despite these successes, the theory contains many unsatisfactory features. The origin of particle masses is a central mystery that has eluded experimental elucidation. In the Standard Model the known particles obtain their mass from the condensate of the so-called Higgs particle. Quantum corrections to the Higgs mass require an unnatural fine tuning in the Higgs mass of one part in 10 -32 to obtain the correct mass scale of electroweak physics. In addition, the origin of the vast hierarchy between the mass scales of the electroweak and quantum gravity physics is not explained in the current theory. Supersymmetric extensions to the Standard Model are not plagued by this fine tuning issue and may therefore be relevant in Nature. In the minimal supersymmetric Standard Model there is also a natural explanation for electroweak symmetry breaking. Supersymmetric Grand Unified Theories also correctly predict a parameter of the Standard Model. This provides non-trivial indirect evidence for these theories. The most general supersymmetric extension to the Standard Model however, is excluded by many physical processes, such as rare flavor changing processes, and the non-observation of the instability of the proton. These processes provide important information about the possible structure such a theory. In particular, certain parameters in this theory must be rather small. A physics explanation for why this is the case would be desirable. It is striking that the gauge couplings of the Standard Model unify if there is supersymmetry close to the weak scale. This suggests that at high energies Nature is described by a supersymmetric Grand Unified Theory. But the mass scale of unification must be introduced into the theory since it does not coincide with the probable mass scale of strong quantum gravity. The subject

Gravitational quantum corrections in warped supersymmetric brane worlds

International Nuclear Information System (INIS)

Gregoire, T.; Rattazzi, R.; Scrucca, C.A.; Strumia, A.; Trincherini, E.

2005-01-01

We study gravitational quantum corrections in supersymmetric theories with warped extra dimensions. We develop for this a superfield formalism for linearized gauged supergravity. We show that the 1-loop effective Kahler potential is a simple functional of the KK spectrum in the presence of generic localized kinetic terms at the two branes. We also present a simple understanding of our results by showing that the leading matter effects are equivalent to suitable displacements of the branes. We then apply this general result to compute the gravity-mediated universal soft mass m 0 2 in models where the visible and the hidden sectors are sequestered at the two branes. We find that the contributions coming from radion mediation and brane-to-brane mediation are both negative in the minimal set-up, but the former can become positive if the gravitational kinetic term localized at the hidden brane has a sizable coefficient. We then compare the features of the two extreme cases of flat and very warped geometry, and give an outlook on the building of viable models

Functional renormalisation group equations for supersymmetric field theories

Energy Technology Data Exchange (ETDEWEB)

Synatschke-Czerwonka, Franziska

2011-01-11

This work is organised as follows: In chapter 2 the basic facts of quantum field theory are collected and the functional renormalisation group equations are derived. Chapter 3 gives a short introduction to the main concepts of supersymmetry that are used in the subsequent chapters. In chapter 4 the functional RG is employed for a study of supersymmetric quantum mechanics, a supersymmetric model which are studied intensively in the literature. A lot of results have previously been obtained with different methods and we compare these to the ones from the FRG. We investigate the N=1 Wess-Zumino model in two dimensions in chapter 5. This model shows spontaneous supersymmetry breaking and an interesting fixed-point structure. Chapter 6 deals with the three dimensional N=1 Wess-Zumino model. Here we discuss the zero temperature case as well as the behaviour at finite temperature. Moreover, this model shows spontaneous supersymmetry breaking, too. In chapter 7 the two-dimensional N=(2,2) Wess-Zumino model is investigated. For the superpotential a non-renormalisation theorem holds and thus guarantees that the model is finite. This allows for a direct comparison with results from lattice simulations. (orig.)

N=2, D=4 supersymmetric σ-models and Hamiltonian mechanics

International Nuclear Information System (INIS)

Galperin, A.; Ogievetsky, V.

1991-05-01

A deep similarity is established between the Hamiltonian mechanics of point particle and supersymmetric N=2, D=4 σ-models formulated within harmonic superspace. An essential part of the latter, the sphere S 2 , comes out as a counterpart of the time variable. (author). 7 refs

Consistent momentum space regularization/renormalization of supersymmetric quantum field theories: the three-loop β-function for the Wess-Zumino model

International Nuclear Information System (INIS)

Carneiro, David; Sampaio, Marcos; Nemes, Maria Carolina; Scarpelli, Antonio Paulo Baeta

2003-01-01

We compute the three loop β function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disentangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories. (author)

Topological field theories and quantum mechanics on commutative space

International Nuclear Information System (INIS)

Lefrancois, M.

2005-12-01

In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)

Quantum mechanics

International Nuclear Information System (INIS)

Anon.

1990-01-01

The book is on quantum mechanics. The emphasis is on the basic concepts and the methodology. The chapters include: Breakdown of classical concepts; Quantum mechanical concepts; Basic postulates of quantum mechanics; solution of problems in quantum mechanics; Simple harmonic oscillator; and Angular Momentum

Two loop effective Kahler potential of (non)-renormalizable supersymmetric models

International Nuclear Information System (INIS)

Groot Nibbelink, S.; Nyawelo, T.S.

2005-10-01

We perform a supergraph computation of the effective Kahler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kahler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kahler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics. (author)

M(atrix) theory: matrix quantum mechanics as a fundamental theory

International Nuclear Information System (INIS)

Taylor, Washington

2001-01-01

This article reviews the matrix model of M theory. M theory is an 11-dimensional quantum theory of gravity that is believed to underlie all superstring theories. M theory is currently the most plausible candidate for a theory of fundamental physics which reconciles gravity and quantum field theory in a realistic fashion. Evidence for M theory is still only circumstantial -- no complete background-independent formulation of the theory exists as yet. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, it has appeared in a different guise as the discrete light-cone quantization of M theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory that reduces to a supersymmetric theory of gravity at low energies. Although its fundamental degrees of freedom are essentially pointlike, higher-dimensional fluctuating objects (branes) arise through the non-Abelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed

Supersymmetric Recipes (1/3)

CERN Multimedia

CERN. Geneva

2011-01-01

In these lectures, I shall describe the theory of supersymmetry accessible to people with a knowledge of basic quantum field theory. The lectures will contain recipes of how to calculate which interactions (and which special relations) are in supersymmetry, without providing detailed proofs of where they come from. We shall also cover: motivation for weak-scale supersymmetry and the minimal supersymmetric standard model.

N=4 supersymmetric mechanics with nonlinear chiral supermultiplet

International Nuclear Information System (INIS)

Bellucci, S.; Beylin, A.; Krivonos, S.; Nersessian, A.; Orazi, E.

2005-01-01

We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system

Pseudoclassical supersymmetrical model for 2+1 Dirac particle

OpenAIRE

Gitman, D. M.; Gonçalves, A. E.; Tyutin, I. V.

1996-01-01

A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle.

Generalized Gelfand-Naimark-Segal construction for supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Fryderyszak, A.; Jakobczyk, L.

1988-01-01

The consistent treatment of anticommuting parameters in quantum theories requires the introduction of the Hilbert Q module with a Q scalar product (where Q is infinite-dimensional Grassman-Banach algebra). The extended GNS construction for representations of Q algebras on such Q modules is given. (orig.)

N=2 supersymmetric dynamics for pedestrians

CERN Document Server

Tachikawa, Yuji

2015-01-01

Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides r...

Extended quantum mechanics

International Nuclear Information System (INIS)

Pavel Bona

2000-01-01

The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics which is related here to some other (more general, but also to more special and 'approximative') theories. Quantum mechanics is here primarily reformulated in an equivalent form of a Poisson system on the phase space consisting of density matrices, where the 'observables', as well as 'symmetry generators' are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfjoint operators. It is shown in this paper that inclusion of additional ('nonlinear') symmetry generators (i. e. 'Hamiltonians') into this reformulation of (linear) quantum mechanics leads to a considerable extension of the theory: two kinds of quantum 'mixed states' should be distinguished, and operator - valued functions of density matrices should be used in the role of 'nonlinear observables'. A general framework for physical theories is obtained in this way: By different choices of the sets of 'nonlinear observables' we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) quantum mechanics, or nonlinear extensions of quantum mechanics; also various 'quasiclassical approximations' to quantum mechanics are all sub theories of the presented extension of quantum mechanics - a version of the extended quantum mechanics. A general interpretation scheme of extended quantum mechanics extending the usual statistical interpretation of quantum mechanics is also proposed. Eventually, extended quantum mechanics is shown to be (included into) a C * -algebraic (hence linear) quantum theory. Mathematical formulation of these theories is presented. The presentation includes an analysis of problems connected with differentiation on infinite-dimensional manifolds, as well as a solution of some problems connected with the work with only densely defined unbounded

Topics in supersymmetric theories

International Nuclear Information System (INIS)

Nemeschansky, D.D.

1984-01-01

This thesis discusses four different topics in supersymmetric theories. In the first part models in which supersymmetry is broken by the Fayet-Iliopoulos mechanism are considered. The possibility that scalar quark and lepton masses might arise radiatively in such theories is explored. In the second part supersymmetric grand unified models with a sliding singlet are considered. The author reviews the argument that the sliding singlet does not work in models with large supersymmetry breaking. Then he considers the possibility of using a sliding singlet with low energy supersymmetry breaking. The third part of the thesis deals with the entropy problem of supersymmetric theories. Most supersymmetric models possess a decoupled particle with mass of order 100 GeV which is copiously produced in the early universe and whose decay produces huge amounts of entropy. The author shows how this problem can be avoided in theories in which the hidden sector contains several light fields. In the fourth part effective Lagrangians for supersymmetric theories are studied. The anomalous pion interaction for supersymmetric theories is written down. General properties of this term are studied both on compact and non-compact manifolds

Applications of quantum mechanical techniques to areas outside of quantum mechanics

CERN Document Server

Khrennikov, Andrei

2018-01-01

This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950's on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is 'quantum probability' and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probabi...

Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for the Feshbach resonance

International Nuclear Information System (INIS)

Sparenberg, Jean-Marc; Samsonov, Boris F; Foucart, Francois; Baye, Daniel

2006-01-01

A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behaviour of solutions at the origin. Contrary to the usual transformations, these 'non-conservative' transformations allow, in the presence of thresholds, the construction of well-behaved potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of the Feshbach-resonance phenomenon. (letter to the editor)

Liouville supersymmetrical equation for a quantum case

International Nuclear Information System (INIS)

Leznov, A.N.; Khrushev, V.V.

1982-01-01

The relation between coupling constants of interacting nonlinear scalar and spinor fields was established which leads to finite series of perturbation theory for the dynamical variable esup(-phi). In the classical limit h/2π→0 the system under consideration turns out to be described by supersymmetric Luiville equation

Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

International Nuclear Information System (INIS)

Ensign, P.W.

1987-01-01

By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem

Engineering quantum mechanics

CERN Document Server

Ahn, Doyeol

2011-01-01

A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...

A supersymmetric matrix model: II. Exploring higher-fermion-number sectors

CERN Document Server

Veneziano, Gabriele

2006-01-01

Continuing our previous analysis of a supersymmetric quantum-mechanical matrix model, we study in detail the properties of its sectors with fermion number F=2 and 3. We confirm all previous expectations, modulo the appearance, at strong coupling, of {\\it two} new bosonic ground states causing a further jump in Witten's index across a previously identified critical 't Hooft coupling $\\lambda_c$. We are able to elucidate the origin of these new SUSY vacua by considering the $\\lambda \\to \\infty$ limit and a strong coupling expansion around it.

Quantum mechanics

CERN Document Server

Rae, Alastair I M

2016-01-01

A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...

Quantum mechanics symmetries

CERN Document Server

Greiner, Walter

1989-01-01

"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...

Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

International Nuclear Information System (INIS)

Golterman, Maarten; Shamir, Yigal

2010-01-01

It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of algebraic renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.

Bubbles of nothing and supersymmetric compactifications

Energy Technology Data Exchange (ETDEWEB)

Blanco-Pillado, Jose J. [IKERBASQUE, Basque Foundation for Science, 48011, Bilbao (Spain); Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Shlaer, Benjamin [Department of Physics, University of Auckland,Private Bag 92019, Auckland (New Zealand); Institute of Cosmology, Department of Physics and Astronomy,Tufts University, Medford, MA 02155 (United States); Sousa, Kepa [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Urrestilla, Jon [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain)

2016-10-03

We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such “topologically unobstructed” cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M{sub 3}×S{sub 1} presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.

Non-Abelian duality in N = 4 supersymmetric gauge theories

International Nuclear Information System (INIS)

Dorey, Nicholas; Fraser, Christophe; Hollowood, Timithy J.; Kneipp, Marco A.C.

1996-03-01

A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-Abelian. The monopole solutions of the theory transform under the non-Abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi monopole configurations in which the long-range non-Abelian fields cancel. In the context of an N = 4 supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture. (author). 39 refs

Quantumness beyond quantum mechanics

International Nuclear Information System (INIS)

Sanz, Ángel S

2012-01-01

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).

Quantum opto-mechanics with micromirrors : combining nano-mechanics with quantum optics

International Nuclear Information System (INIS)

Groeblacher, S.

2010-01-01

This work describes more than four years of research on the effects of the radiation-pressure force of light on macroscopic mechanical structures. The basic system studied here is a mechanical oscillator that is highly reflective and part of an optical resonator. It interacts with the optical cavity mode via the radiation-pressure force. Both the dynamics of the mechanical oscillation and the properties of the light field are modified through this interaction. In our experiments we use quantum optical tools (such as homodyning and down-conversion) with the goal of ultimately showing quantum behavior of the mechanical center of mass motion. In this thesis we present several experiments that pave the way towards this goal and when combined should allow the demonstration of the envisioned quantum phenomena, including entanglement, teleportation and Schroeodinger cat states. The study of quantum behavior of truly macroscopic systems is a long outstanding goal, which will help to answer some of the most fundamental questions in quantum physics today: Why is the world around us classical and not quantum? Is there a size- or mass-limit to systems for them to behave according to quantum mechanics? Is quantum theory complete or do we have to extend it to include mechanisms such as decoherence? Can we use the quantum nature of macroscopic objects to, for example, improve the measurement precision of classical apparatuses? The experiments discussed in this thesis include the very first passive radiation-pressure cooling of a mechanical oscillator in a cryogenic optical resonator, as well as the experimental demonstration of radiation-pressure cooling close to the mechanical quantum ground state. Cooling of the mechanical motion is an important pre-condition for observing quantum effects of the mechanical oscillator. In another experiment, we have demonstrated that we are able to enter the strong-coupling regime of the optomechanical system a regime where coherent energy

Supersymmetric AdS3, AdS2 and bubble solutions

International Nuclear Information System (INIS)

Gauntlett, Jerome P.; Waldram, Daniel; Kim, Nakwoo

2007-01-01

We present new supersymmetric AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity. The former are dual to conformal field theories in two dimensions with N = (0, 2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS 2 solutions of D = 11 supergravity that have non-compact internal spaces which are dual to three-dimensional N = 2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries

Quantum mechanics

International Nuclear Information System (INIS)

Rae, A.I.M.

1981-01-01

This book, based on a thirty lecture course given to students at the beginning of their second year, covers the quantum mechanics required by physics undergraduates. Early chapters deal with wave mechanics, including a discussion of the energy states of the hydrogen atom. These are followed by a more formal development of the theory, leading to a discussion of some advanced applications and an introduction to the conceptual problems associated with quantum measurement theory. Emphasis is placed on the fundamentals of quantum mechanics. Problems are included at the end of each chapter. (U.K.)

Quantum mechanics

CERN Document Server

Powell, John L

2015-01-01

Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ

The spectra of supersymmetric states in string theory

NARCIS (Netherlands)

Cheng, M.C.N.

2008-01-01

In this thesis we study the spectra of supersymmetric states in string theory compactifications with eight and sixteen supercharges, with special focus placed on the quantum states of black holes and the phenomenon of wall-crossing in these theories. A self-contained introduction to the relevant

Emergent mechanics, quantum and un-quantum

Science.gov (United States)

Ralston, John P.

2013-10-01

There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

Fractional quantum mechanics

CERN Document Server

Laskin, Nick

2018-01-01

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

Super-quantum curves from super-eigenvalue models

Energy Technology Data Exchange (ETDEWEB)

Ciosmak, Paweł [Faculty of Mathematics, Informatics and Mechanics, University of Warsaw,ul. Banacha 2, 02-097 Warsaw (Poland); Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, 30-348 Kraków (Poland); Manabe, Masahide [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Sułkowski, Piotr [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E. California Blvd, Pasadena, CA 91125 (United States)

2016-10-10

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

International Nuclear Information System (INIS)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-01-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

Science.gov (United States)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-10-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/ β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Stochastic quantization of field theories on the lattice and supersymmetrical models

International Nuclear Information System (INIS)

Aldazabal, Gerardo.

1984-01-01

Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es

From topological quantum field theories to supersymmetric gauge theories

International Nuclear Information System (INIS)

Bossard, G.

2007-10-01

This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

Quantum mechanics with quantum time

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

Using a non-canonical Lie structure of classical mechanics a new algebra of quantum mechanical observables is constructed. The new algebra, in addition to the notion of classical time, makes it possible to introduce the notion of quantum time. A new type of uncertainty relation is derived. (author)

Supersymmetric type-III seesaw mechanism: Lepton flavor violation and LHC phenomenology

OpenAIRE

Hirsch, Martin; Porod, Werner; Staub, Florian; Weiss, Christian H.

2013-01-01

We study a supersymmetric version of the type-III seesaw mechanism considering two variants of the model: a minimal version for explaining neutrino data with only two copies of 24 superfields and a model with three generations of 24-plets. The latter predicts, in general, rates for mu -> e gamma inconsistent with experimental data. However, this bound can be evaded if certain special conditions within the neutrino sector are fulfilled. In the case of two 24-plets, lepton flavor violation cons...

Brane/Flux Annihilation and the String Dual of a Non-Supersymmetric Field Theory

International Nuclear Information System (INIS)

Kachru, Shamit

2002-01-01

We consider the dynamics of p anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S 3 . We find that for p << M the system relaxes to a nonsupersymmetric NS 5-brane ''giant graviton'' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M - p D3 branes. This decay mode is exponentially suppressed and proceeds via the nucleation of an NS 5-brane bubble wall. They propose a dual field theory interpretation of the decay as the transition between a nonsupersymmetric baryonic branch and a supersymmetric mesonic branch of the corresponding SU(2M-p) x SU(M-p) low energy gauge theory. The NS 5-brane tunneling process also provides a simple visualization of the geometric transition by which D3-branes can dissolve into 3-form flux

Advanced Visual Quantum Mechanics

CERN Document Server

Thaller, Bernd

2005-01-01

Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.

Quantum mechanics. An introduction

International Nuclear Information System (INIS)

Lesch, H.

2008-01-01

The following topics are dealt with: The way to quantum mechanics starting from thermal radiation and the stability of matter, Heisenberg's uncertainty relation, the impact of quantum mechanics on technology, the description of the big bang by means of quantum mechanics

Quantum mechanics

CERN Document Server

Fitzpatrick, Richard

2015-01-01

Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.

Classicality in quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Dreyer, Olaf [Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ (United Kingdom)

2007-05-15

In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity.

Classicality in quantum mechanics

International Nuclear Information System (INIS)

Dreyer, Olaf

2007-01-01

In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity

Aspects of supersymmetric inflation

International Nuclear Information System (INIS)

Lindblom, P.R.

1987-01-01

A new supersymmetric inflationary model is presented and shown to possess the following features: a successful slow rollover produced by quantum corrections; an acceptable pattern of supersymmetry breaking leading to the correct value of the electroweak scale; and a stable slow rollover transition to a minimum with vanishing cosmological constant. It is demonstrated that there is a class of GUT models which are compatible with an inflationary universe scenario in which: (a) the GUT and inflationary phase transitions are distinct (as in supersymmetric inflation); and (b) an observable number of GUT monopoles are created thermally due to reheating of the GUT sector after inflation. This provides one of the few ways of reconciling an observation of GUT monopoles with inflation. New techniques are developed for constructing inflationary models with multiple inflation fields, such as generalizing the one-dimensional slow rollover constraints and estimating the contribution to δρ/ρ from fluctuations transverse to the path of the slow rollover. A new method for ending the slow rollover portion of the inflationary transition is developed

Relativistic quantum mechanics

International Nuclear Information System (INIS)

Ollitrault, J.Y.

1998-12-01

These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.)

Quantum mechanics for pedestrians

CERN Document Server

Pade, Jochen

2014-01-01

This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...

Two new supersymmetric equations of Harry Dym type and their supersymmetric reciprocal transformations

International Nuclear Information System (INIS)

Tian, Kai; Liu, Q.P.

2012-01-01

A new N=1 supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed. -- Highlights: ► A new supersymmetric Harry Dym equation is constructed through supersymmetric reciprocal transformations. ► The recursion operator and Lax formulation are established for the new supersymmetric Harry Dym equation. ► A supersymmetric equation of Harry Dym type is shown to be linearized through supersymmetric reciprocal transformation.

Why quantum mechanics?

International Nuclear Information System (INIS)

Landsberg, P.T.

1988-01-01

It is suggested that an oversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of a classical uncertainty relation for a very simple model. The existence of universal motion, i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter

Quantifying Quantum-Mechanical Processes.

Science.gov (United States)

Hsieh, Jen-Hsiang; Chen, Shih-Hsuan; Li, Che-Ming

2017-10-19

The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of the natural world, from understanding counter-intuitive concepts to the development of wholly quantum-mechanical technology. Here, we show that quantum-mechanical processes can be quantified using a generic classical-process model through which any classical strategies of mimicry can be ruled out. We demonstrate the success of this formalism using fundamental processes postulated in quantum mechanics, the dynamics of open quantum systems, quantum-information processing, the fusion of entangled photon pairs, and the energy transfer in a photosynthetic pigment-protein complex. Since our framework does not depend on any specifics of the states being processed, it reveals a new class of correlations in the hierarchy between entanglement and Einstein-Podolsky-Rosen steering and paves the way for the elaboration of a generic method for quantifying physical processes.

Studies on quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Zhang, S.

1987-01-01

This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather from a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable

Classical Mechanics as Nonlinear Quantum Mechanics

International Nuclear Information System (INIS)

Nikolic, Hrvoje

2007-01-01

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics

Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos

OpenAIRE

Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.

2001-01-01

We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.

Prologue to super quantum mechanics something is rotten in the state of quantum mechanics

CERN Document Server

Vaguine, Victor

2012-01-01

Since its foundation more than eight decades ago, quantum mechanics has been plagued by enigmas, mysteries and paradoxes and held hostage by quantum positivism. This fact strongly suggests that something is fundamentally wrong with the quantum mechanics paradigm. The best scientific minds, such as Albert Einstein, Louis de Broglie, David Bohm, Richard Feynman and others have spent years of their professional lives attempting to find resolution to the quantum mechanics predicament, with not much success. A shift of the quantum mechanics paradigm toward a deeper physics theory is long overdue.

Defect networks and supersymmetric loop operators

Energy Technology Data Exchange (ETDEWEB)

Bullimore, Mathew [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada)

2015-02-10

We consider topological defect networks with junctions in A{sub N−1} Toda CFT and the connection to supersymmetric loop operators in N=2 theories of class S on a four-sphere. Correlation functions in the presence of topological defect networks are computed by exploiting the monodromy of conformal blocks, generalising the notion of a Verlinde operator. Concentrating on a class of topological defects in A{sub 2} Toda theory, we find that the Verlinde operators generate an algebra whose structure is determined by a set of generalised skein relations that encode the representation theory of a quantum group. In the second half of the paper, we explore the dictionary between topological defect networks and supersymmetric loop operators in the N=2{sup ∗} theory by comparing to exact localisation computations. In this context, the the generalised skein relations are related to the operator product expansion of loop operators.

p-Adic quantum mechanics

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1988-01-01

Quantum mechanics above the field of p-adic numbers is constructed. Three formulations of p-adic quantum mechanics are considered: 1) quantum mechanics with complex-valued wave functions and p-adic coordinates and pulses; an approach based on Weyl representation is suggested; 2) the probability (Euclidean) formulation; 3) the secondary quantization representation (Fock representation) with p-adic wave functions

Quantum Mechanics: Fundamentals; Advanced Quantum Mechanics; Mathematical Concepts of Quantum Mechanics

International Nuclear Information System (INIS)

Whitaker, A

2004-01-01

This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding. The

Testing Nonassociative Quantum Mechanics.

Science.gov (United States)

Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

2015-11-27

The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

Manin's quantum spaces and standard quantum mechanics

International Nuclear Information System (INIS)

Floratos, E.G.

1990-01-01

Manin's non-commutative coordinate algebra of quantum groups is shown to be identical, for unitary coordinates, with the conventional operator algebras of quantum mechanics. The deformation parameter q is a pure phase for unitary coordinates. When q is a root of unity. Manin's algebra becomes the matrix algebra of quantum mechanics for a discretized and finite phase space. Implications for quantum groups and the associated non-commutative differential calculus of Wess and Zumino are discussed. (orig.)

Quantum mechanics

CERN Document Server

Ghosh, P K

2014-01-01

Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.

Understand quantum mechanics

International Nuclear Information System (INIS)

Omnes, R.

2000-01-01

The author presents the interpretation of quantum mechanics in a simple and direct way. This book may be considered as a complement of specialized books whose aim is to present the mathematical developments of quantum mechanics. As early as the beginning of quantum theory, Bohr, Heisenberg and Pauli proposed the basis of what is today called the interpretation of Copenhagen. This interpretation is still valid but 2 important discoveries have led to renew some aspects of the interpretation of Copenhagen. The first one was the discovery of the decoherence phenomenon which is responsible for the absence of quantum interferences in the macroscopic world. The second discovery was the achievement of the complete derivation of classical physics from quantum physics, it means that the classical determinism fits in the framework of quantum probabilism. A short summary ends each chapter. (A.C.)

Introduction to quantum mechanics

CERN Document Server

Phillips, A C

2003-01-01

Introduction to Quantum Mechanics is an introduction to the power and elegance of quantum mechanics. Assuming little in the way of prior knowledge, quantum concepts are carefully and precisely presented, and explored through numerous applications and problems. Some of the more challenging aspects that are essential for a modern appreciation of the subject have been included, but are introduced and developed in the simplest way possible.Undergraduates taking a first course on quantum mechanics will find this text an invaluable introduction to the field and help prepare them for more adv

Lectures on Quantum Mechanics

CERN Document Server

Dirac, Paul Adrien Maurice

1964-01-01

The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered

Quantum mechanics the theoretical minimum

CERN Document Server

Susskind, Leonard

2014-01-01

From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

Relativistic Quantum Mechanics

International Nuclear Information System (INIS)

Antoine, J-P

2004-01-01

The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic

Vector supersymmetric multiplets in two dimensions

International Nuclear Information System (INIS)

Khattab, Mohammad

1990-01-01

Author.The invariance of both, N=1 supersymmetric yang-Mills theory and N-1 supersymmetric off-shell Wess-Zumino model in four dimensions is proved. Dimensional reduction is then applied to obtain super Yang-Mills theory with extended supersymmetry, N=2, in two dimensions. The resulting theory is then truncated to N=1 super Yang-Mills and with further truncation, N=1/2 supersymmetry is shown to be possible. Then, using the duality transformations, we find the off-shell supersymmetry algebra is closed and that the auxiliary fields are replaced by four-rank antisymmetric tensors with Gauge symmetry. Finally, the mechanism of dimensional reduction is then applied to obtain N=2 extended off-shell supersymmetric model with two gauge vector fields

Quantum mechanics theory and experiment

CERN Document Server

Beck, Mark

2012-01-01

This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...

Three-space from quantum mechanics

International Nuclear Information System (INIS)

Chew, G.F.; Stapp, H.P.

1988-01-01

We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically

Supersymmetric Hamiltonian approach to edge excitations in ν=5/2 fractional quantum Hall effect

International Nuclear Information System (INIS)

Yu Ming; Zhang Xin

2008-01-01

A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, an N=2 supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore-Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also found that the excited states in our model looks similar but not exactly the same as Moore and Read's

The essentials of quantum mechanics

International Nuclear Information System (INIS)

Omnes, R.

2006-09-01

This book is an introduction to quantum mechanics, the author explains the foundation, interpretation and today limits of this science. The consequences of quantum concepts are reviewed through the lens of recent experimental data. In that way, issues like wave-particle duality, uncertainty principle, decoherence, relationship with classical mechanics or the unicity of reality, issues that were difficult to grasp before, appear now clearer. The book has been divided into 8 chapters: 1) possibility and chance, 2) quantum formalism, 3) fundamental quantum concepts, 4) how to deal with quantum mechanics, 5) decoherence theory, 6) the quantum logic system, 7) the emergence of classical physics, and 8) quantum measurements. (A.C.)

The emerging quantum the physics behind quantum mechanics

CERN Document Server

Pena, Luis de la; Valdes-Hernandez, Andrea

2014-01-01

This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics.  The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...

Bananaworld quantum mechanics for primates

CERN Document Server

Bub, Jeffrey

2016-01-01

What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...

Physics: quantum mechanics

International Nuclear Information System (INIS)

Basdevant, J.L.

1983-01-01

From important experiment descriptions (sometimes, intentionally simplified), the essential concepts in Quantum Mechanics are first introduced. Wave function notion is described, Schroedinger equation is established, and, after applications rich in physical signification, quantum state and Hilbert space formalism are introduced, which will help to understand many essential phenomena. Then the quantum mechanic general formulation is written and some important consequences are deduced. This formalism is applied to a simple physical problem series (angular momentum, hydrogen atom, etc.) aiming at assimilating the theory operation and its application [fr

Quantum mechanics

International Nuclear Information System (INIS)

Basdevant, J.L.; Dalibard, J.; Joffre, M.

2008-01-01

All physics is quantum from elementary particles to stars and to the big-bang via semi-conductors and chemistry. This theory is very subtle and we are not able to explain it without the help of mathematic tools. This book presents the principles of quantum mechanics and describes its mathematical formalism (wave function, Schroedinger equation, quantum operators, spin, Hamiltonians, collisions,..). We find numerous applications in the fields of new technologies (maser, quantum computer, cryptography,..) and in astrophysics. A series of about 90 exercises with their answers is included. This book is based on a physics course at a graduate level. (A.C.)

Quantum gravity

International Nuclear Information System (INIS)

Isham, C.

1989-01-01

Gravitational effects are seen as arising from a curvature in spacetime. This must be reconciled with gravity's apparently passive role in quantum theory to achieve a satisfactory quantum theory of gravity. The development of grand unified theories has spurred the search, with forces being of equal strength at a unification energy of 10 15 - 10 18 GeV, with the ''Plank length'', Lp ≅ 10 -35 m. Fundamental principles of general relativity and quantum mechanics are outlined. Gravitons are shown to have spin-0, as mediators of gravitation force in the classical sense or spin-2 which are related to the quantisation of general relativity. Applying the ideas of supersymmetry to gravitation implies partners for the graviton, especially the massless spin 3/2 fermion called a gravitino. The concept of supersymmetric strings is introduced and discussed. (U.K.)

Conceptual foundations of quantum mechanics

International Nuclear Information System (INIS)

Shimony, A.

1989-01-01

Radical innovation in the quantum mechanical framework such as objective indefiniteness, objective chance, objective probability, potentiality, entanglement and quantum nonlocality are discussed and related to the standard formalism. Examples are given which though problematic in classical mechanics are simply explained with these new concepts. Evidence is presented that the conceptual innovations of quantum mechanics cannot be separated from its predictive power. Proposals for solving ''the reduction of the wave packet'' anomaly are presented. Further radical innovations in quantum mechanics are anticipated. (U.K.)

Quantum mechanics. 2. printing (paperback).

International Nuclear Information System (INIS)

Lipkin, H.J.

1986-01-01

Intended for a first year graduate course in quantum mechanics, this collection of topics can also be considered as a set of self-contained 'monographs for pedestrians' on the Moessbauer effect, many-body quantum mechanics, kaon physics, scattering theory, Feynman diagrams, symmetries and relativistic quantum mechanics. (Auth.)

Questioning quantum mechanics

Science.gov (United States)

Frappier, Mélanie

2018-03-01

A century after its inception, quantum mechanics continues to puzzle us with dead-and-alive cats, waves "collapsing" into particles, and "spooky action at a distance." In his first book, What Is Real?, science writer and astrophysicist Adam Becker sets out to explore why the physics community is still arguing today about quantum mechanics's true meaning.

Quantum confinement in hydrogen bond of DNA and RNA

International Nuclear Information System (INIS)

Dos Santos, C S; Filho, E Drigo; Ricotta, R M

2015-01-01

The hydrogen bond is a fundamental ingredient to stabilize the DNA and RNA macromolecules. The main contribution of this work is to describe quantitatively this interaction as a consequence of the quantum confinement of the hydrogen. The results for the free and confined system are compared with experimental data. The formalism to compute the energy gap of the vibration motion used to identify the spectrum lines is the Variational Method allied to Supersymmetric Quantum Mechanics. (papert)

Learning quantum field theory from elementary quantum mechanics

International Nuclear Information System (INIS)

Gosdzinsky, P.; Tarrach, R.

1991-01-01

The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem

Non-relativistic quantum mechanics

CERN Document Server

Puri, Ravinder R

2017-01-01

This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...

Quantum mechanics in chemistry

CERN Document Server

Schatz, George C

2002-01-01

Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt

Proceedings of quantum field theory, quantum mechanics, and quantum optics

International Nuclear Information System (INIS)

Dodonov, V.V.; Man; ko, V.I.

1991-01-01

This book contains papers presented at the XVIII International Colloquium on Group Theoretical Methods in Physics held in Moscow on June 4-9, 1990. Topics covered include; applications of algebraic methods in quantum field theory, quantum mechanics, quantum optics, spectrum generating groups, quantum algebras, symmetries of equations, quantum physics, coherent states, group representations and space groups

Relational quantum mechanics

International Nuclear Information System (INIS)

Rovelli, C.

1996-01-01

I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the open-quotes measurement problemclose quotes) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of open-quotes observer-independent stateclose quotes of a system, or open-quotes observer-independent values of physical quantities.close quotes I reformulate the problem of the open-quotes interpretation of quantum mechanicsclose quotes as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete

Quantum mechanics II advanced topics

CERN Document Server

Rajasekar, S

2015-01-01

Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.

Quantum Mechanics for Electrical Engineers

CERN Document Server

Sullivan, Dennis M

2011-01-01

The main topic of this book is quantum mechanics, as the title indicates.  It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory.   It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions.  Two key features make this book different from others on quantum mechanics, even those usually intended for engineers:   First, after a brief introduction, much of the development is through Fourier theory, a topic that is at

Quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Analogies between classical statistical mechanics and quantum mechanics

International Nuclear Information System (INIS)

Uehara, M.

1986-01-01

Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

Supersymmetric flipped SU(5) revitalized

Energy Technology Data Exchange (ETDEWEB)

Antoniadis, I.; Ellis, J.; Hagelin, J.S.; Nanopoulos, D.V.

1987-08-06

We describe a simple N = 1 supersymmetric GUT based on the group SU(5) x U(1) which has the following virtues: the gauge group is broken down to the SU(3)/sub C/ x SU(2)/sub L/ x U(1)/sub y/ of the standard model using just 10, 10 Higgs representations, and the doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin/sup 2/theta/sub w/ can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring.

Quantum mechanics with non-negative quantum distribution function

International Nuclear Information System (INIS)

Zorin, A.V.; Sevastianov, L.A.

2010-01-01

Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

M-Theory and Maximally Supersymmetric Gauge Theories

CERN Document Server

Lambert, Neil

2012-01-01

In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.

Statistical ensembles in quantum mechanics

International Nuclear Information System (INIS)

Blokhintsev, D.

1976-01-01

The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)

Science.gov (United States)

Cataloglu, Erdat

The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p important factor for students in acquiring a successful understanding of quantum mechanics.

Supersymmetric color superconductivity

International Nuclear Information System (INIS)

Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi

2003-01-01

Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N c ) gauge theories with N f flavors of quarks in the presence of a baryon chemical potential μ, and describe the global symmetry breaking patterns at low energy. Our analysis requires μ > Λ. We find that for N F c a modified U(1) B symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N f = N c there is a critical chemical potential above which the U(1) B is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N c + 1 (le) N f c and find that baryon number is broken dynamically for μ > μ c . We also give a qualitative description of the phases in the ''conformal window'', 3/2 N c f c , at finite density

Supersymmetric color superconductivity

International Nuclear Information System (INIS)

Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi

2004-01-01

Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N c ) gauge theories with N f flavors of quarks in the presence of a baryon chemical potential mu, and describe the global symmetry breaking patterns at low energy. Our analysis requires μ f c a modified U(1) B symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N f =N c there is a critical chemical potential above which the U(1) B is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N c +1≤ N f c and find that baryon number is broken dynamically for μ > mu c . We also give a qualitative description of the phases in the 'conformal window', 3/2 N c f c , at finite density. (author)

A textbook of quantum mechanics

International Nuclear Information System (INIS)

Mathews, P.M.; Venkatesan, K.

1977-01-01

After briefly surveying the inadequacy of the classical ideas and elementary older quantum theory, the ideas of wave mechanics, the postulates of quantum mechanics, exactly soluble problems, approximation techniques, scattering theory, angular momentum, time dependent problems and the basic ideas of relativistic quantum mechanics are discussed. The book is meant for the Master of Science degree course students of Indian Universities. (M.G.B.)

Fundamentals of Quantum Mechanics

Science.gov (United States)

Tang, C. L.

2005-06-01

Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner emphasising applications in solid state electronics and modern optics. Following a logical sequence, the book is focused on the key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most important applications in modern semiconductor electronics and optics. Containing many homework problems and worked examples, the book is suitable for senior-level undergraduate and graduate level students in electrical engineering, materials science and applied physics. Clear exposition of quantum mechanics written in a concise and accessible style Precise physical interpretation of the mathematical foundations of quantum mechanics Illustrates the important concepts and results by reference to real-world examples in electronics and optoelectronics Contains homeworks and worked examples, with solutions available for instructors

Locality and quantum mechanics.

Science.gov (United States)

Unruh, W G

2018-07-13

It is argued that it is best not to think of quantum mechanics as non-local, but rather that it is non-realistic.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Problems in quantum mechanics

CERN Document Server

Goldman, Iosif Ilich; Geilikman, B T

2006-01-01

This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.

Black hole microstates in AdS{sub 4} from supersymmetric localization

Energy Technology Data Exchange (ETDEWEB)

Benini, Francesco [Blackett Laboratory, Imperial College London,South Kensington Campus, London SW7 2AZ (United Kingdom); International School for Advanced Studies (SISSA),via Bonomea 265, 34136 Trieste (Italy); Hristov, Kiril [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,Tsarigradsko Chaussee 72, 1784 Sofia (Bulgaria); Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,piazza della Scienza 3, I-20126 Milano (Italy); INFN, sezione di Milano-Bicocca,piazza della Scienza 3, I-20126 Milano (Italy)

2016-05-10

This paper addresses a long standing problem, the counting of the microstates of supersymmetric asymptotically AdS black holes in terms of a holographically dual field theory. We focus on a class of asymptotically AdS{sub 4} static black holes preserving two real supercharges which are dual to a topologically twisted deformation of the ABJM theory. We evaluate in the large N limit the topologically twisted index of the ABJM theory and we show that it correctly reproduces the entropy of the AdS{sub 4} black holes. An extremization of the index with respect to a set of chemical potentials is required. We interpret it as the selection of the exact R-symmetry of the superconformal quantum mechanics describing the horizon of the black hole.

Quantum mechanics and Bell's inequalities

International Nuclear Information System (INIS)

Jones, R.T.; Adelberger, E.G.

1994-01-01

Santos argues that, if one interprets probabilities as ratios of detected events to copies of the physical system initially prepared, the quantum mechanical predictions for the classic tests of Bell's inequalities do not violate the inequalities. Furthermore, he suggests that quantum mechanical states which do violate the inequalities are not physically realizable. We discuss a physically realizable experiment, meeting his requirements, where quantum mechanics does violate the inequalities

On obtaining classical mechanics from quantum mechanics

International Nuclear Information System (INIS)

Date, Ghanashyam

2007-01-01

Constructing a classical mechanical system associated with a given quantum-mechanical one entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum-mechanical system naturally has the structure of an infinite-dimensional symplectic manifold ('quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straightforwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and one recovers the linear classical phase space R 2N . We report on how the procedure also allows extraction of nonlinear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality

Using supermodels in quantum optics

Directory of Open Access Journals (Sweden)

Garbers Nicole

2006-01-01

Full Text Available Starting from supersymmetric quantum mechanics and related supermodels within Schrödinger theory, we review the meaning of self-similar superpotentials which exhibit the spectrum of a geometric series. We construct special types of discretizations of the Schrödinger equation on time scales with particular symmetries. This discretization leads to the same type of point spectrum for the referred Schrödinger difference operator than in the self-similar superpotential case, hence exploiting an isospectrality situation. A discussion is opened on the question of how the considered energy sequence and its generalizations serve the understanding of coherent states in quantum optics.

Chiral rings and anomalies in supersymmetric gauge theory

International Nuclear Information System (INIS)

Cachazo, Freddy; Witten, Edward; Seiberg, Nathan; Douglas, Michael R.

2002-01-01

Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of 'integration constants'. From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of N=1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate. (author)

Quantum mechanics by walking 1. Foundations

International Nuclear Information System (INIS)

Pade, Jochen

2012-01-01

Quantum mechanics by walking introduces to the foundations of non-relativistic quantum mechanics. This book applies to studyings of teaching physics as well as all studyings of physics, who look for an appropriate, easy, fresh, and modern approach to the field. In the present first volume the essential principles of quantum mechanics are worked out. in order to be able to develop their mathematical formulation as fastly and clearly as possible, systematically between wave mechanics and algebraic presentation is changed. Beside themes, which are traditionally in textbooks of quantum mechanics, extensively actual aspects like interaction-free quantum measurement, neutrino oscillations, or quantum cryptography are considered as well as fundamental problems and epistemological questions discussed, as they occur in connection with the measurement process. The list of the postulates of quantum mechanics closes this volume; they form the framework for the extensions and applications, which are discussed in the second volume. The required mathematical aids are introduced step by step. In the appendix the most important mathematical tools are compactly collected, so that supplementing literature can be far reachingly abandoned. Furthermore in the appendix supplementing themes are deepened as for instance the Quantum Zeno effect or delayed-choice experiments.

Analytical mechanics for relativity and quantum mechanics

CERN Document Server

Johns, Oliver Davis

2011-01-01

Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...

Supersymmetric leptogenesis with a light hidden sector

International Nuclear Information System (INIS)

De Simone, Andrea

2010-04-01

Supersymmetric scenarios incorporating thermal leptogenesis as the origin of the observed matter-antimatter asymmetry generically predict abundances of the primordial elements which are in conflict with observations. In this paper we pro- pose a simple way to circumvent this tension and accommodate naturally ther- mal leptogenesis and primordial nucleosynthesis. We postulate the existence of a light hidden sector, coupled very weakly to the Minimal Supersymmetric Standard Model, which opens up new decay channels for the next-to-lightest supersymmetric particle, thus diluting its abundance during nucleosynthesis. We present a general model-independent analysis of this mechanism as well as two concrete realizations, and describe the relevant cosmological and astrophysical bounds and implications for this dark matter scenario. Possible experimental signatures at colliders and in cosmic-ray observations are also discussed. (orig.)

Spontaneous baryogenesis in supersymmetric models

International Nuclear Information System (INIS)

Abel, S.A.; Cottingham, W.N.; Whittingham, I.B.

1993-01-01

In this paper we extent the results of previous work on spontaneous baryogenesis to general models involving charge-parity (CP) violation in the Higgs sector. We show how to deal with Chern-Simons terms appearing in the effective potential arising from phase changes in the vacuum expectation values of the Higgs fields. In particular, this enables us to apply this mechanism to general supersymmetric models including the minimal supersymmetric standard model, and the extended model with a gauge singlet. A comparison is made between this approach, and that in which one solves the equations of motion for Higgs winding modes. As anticipated in earlier work, the effect of the latter approach is found to be small. (Author)

From wave mechanics to quantum chemistry

International Nuclear Information System (INIS)

Daudel, R.

1996-01-01

The origin of wave mechanics, which is now called quantum mechanics, is evoked. The main stages of the birth of quantum chemistry are related as resulting from the application of quantum mechanics to the study of molecular properties and chemical reactions. (author). 14 refs

Quantum mechanics and quantum information a guide through the quantum world

CERN Document Server

Fayngold, Moses

2013-01-01

Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.

Geometric Aspects of Quantum Mechanics and Quantum Entanglement

International Nuclear Information System (INIS)

Chruscinski, Dariusz

2006-01-01

It is shown that the standard non-relativistic Quantum Mechanics gives rise to elegant and rich geometrical structures. The space of quantum states is endowed with nontrivial Fubini-Study metric which is responsible for the 'peculiarities' of the quantum world. We show that there is also intricate connection between geometrical structures and quantum entanglement

Modern logic and quantum mechanics

International Nuclear Information System (INIS)

Garden, R.W.

1984-01-01

The book applies the methods of modern logic and probabilities to ''interpreting'' quantum mechanics. The subject is described and discussed under the chapter headings: classical and quantum mechanics, modern logic, the propositional logic of mechanics, states and measurement in mechanics, the traditional analysis of probabilities, the probabilities of mechanics and the model logic of predictions. (U.K.)

Research of supersymmetric particles in the experience H1; Recherche de particules supersymetriques dans l`experience H1

Energy Technology Data Exchange (ETDEWEB)

Perez, E

1996-06-17

The study exposed in this thesis concerns a supersymmetrical extension of the Standard Model where the R-parity (a new quantum number) is not conserved. The principle results, how this analysis can be generalised and what it is possible to get with more luminosity are detailed; then, the potential for HERA to produce others kind of supersymmetric particles is shown. (N.C.). 98 refs., 146 figs., 17 tabs.

Quantum mechanics a fundamental approach

CERN Document Server

Wan, K Kong

2018-01-01

The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning. This makes it difficult to appreciate the mathematical formalism and hampers the understanding of quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. Quantum mechanics is presented in six groups of postulates. A chapter is devoted to each group of postulates with a detailed discussion. Systems with superselection rules, and some conceptual issues such as quantum paradoxes and measurement, are also discussed. The book conc...

Logical foundation of quantum mechanics

International Nuclear Information System (INIS)

Stachow, E.W.

1980-01-01

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to a dialogic semantics that is adequate in the case of a formal language for quantum physics. The system of sequential logic which is comprised by the language is more general than classical logic; it includes the classical system as a special case. Although the system of sequential logic can be founded without reference to the empirical content of quantum physical propositions, it establishes an essential part of the structure of the mathematical formalism used in quantum mechanics. It is the purpose of this paper to demonstrate the connection between the formal language of quantum physics and its representation by mathematical structures in a self-contained way. (author)

Bell's theorem and quantum mechanics

Science.gov (United States)

Rosen, Nathan

1994-02-01

Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor

Nonlocal quantum field theory and stochastic quantum mechanics

International Nuclear Information System (INIS)

Namsrai, K.

1986-01-01

This volume presents a systematic development of the implications to both quantum mechanics and quantum field theory of the hypothesis of a stochastic structure of space-time. Some applications to elementary particle physics are also considered. Part 1 is concerned with nonlocal quantum field theory and, among other topics, deals with quantized fields, electromagnetic and weak processes, the Schroedinger equation, and functional methods and their applications. Part 2 presents an introduction to stochastic mechanics and many specific problems of interest are discussed. (Auth.)

Supersymmetric reciprocal transformation and its applications

International Nuclear Information System (INIS)

Liu, Q. P.; Popowicz, Ziemowit; Tian Kai

2010-01-01

The supersymmetric analog of the reciprocal transformation is introduced. This is used to establish a transformation between one of the supersymmetric Harry Dym equations and the supersymmetric modified Korteweg-de Vries equation. The reciprocal transformation, as a Baecklund-type transformation between these two equations, is adopted to construct a recursion operator for the supersymmetric Harry Dym equation. By proper factorization of the recursion operator, a bi-Hamiltonian structure is found for the supersymmetric Harry Dym equation. Furthermore, a supersymmetric Kawamoto equation is proposed and is associated with the supersymmetric Sawada-Kotera equation. The recursion operator and odd bi-Hamiltonian structure of the supersymmetric Kawamoto equation are also constructed.

Learn Quantum Mechanics with Haskell

Directory of Open Access Journals (Sweden)

Scott N. Walck

2016-11-01

Full Text Available To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The laboratory ideas are naturally expressed in one language, and the theoretical ideas in another. We present a method for learning quantum mechanics that begins with a laboratory language for the description and simulation of simple but essential laboratory experiments, so that students can gain some intuition about the phenomena that a theory of quantum mechanics needs to explain. Then, in parallel with the introduction of the mathematical framework on which quantum mechanics is based, we introduce a calculational language for describing important mathematical objects and operations, allowing students to do calculations in quantum mechanics, including calculations that cannot be done by hand. Finally, we ask students to use the calculational language to implement a simplified version of the laboratory language, bringing together the theoretical and laboratory ideas.

Emergent quantum mechanics without wavefunctions

Science.gov (United States)

Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

2016-03-01

We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

Search for violations of quantum mechanics

International Nuclear Information System (INIS)

Ellis, J.; Hagelin, J.S.; Nanopoulos, D.V.; Srednicki, M.

1984-01-01

The treatment of quantum effects in gravitational fields indicates that pure states may evolve into mixed states, and Hawking has proposed modification of the axioms of field theory which incorporate the corresponding violation of quantum mechanics. In this paper we propose a modified hamiltonian equation of motion for density matrices and use it to interpret upper bounds on the violation of quantum mechanics in different phenomenological situations. We apply our formalism to the K 0 -anti K 0 system and to long baseline neutron interferometry experiments. In both cases we find upper bounds of about 2x10 -21 GeV on contributions to the single particle 'hamiltonian' which violate quantum mechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantum mechanics. An appendix contains model estimates of the magnitude of effects violating quantum mechanics. (orig.)

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

International Nuclear Information System (INIS)

Clarke, M L

2014-01-01

The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism). (paper)

Fundamentals of quantum mechanics

CERN Document Server

House, J E

2017-01-01

Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.

Topological field theories and quantum mechanics on commutative space; Theories des champs topologiques et mecanique quantique en espace non-commutatif

Energy Technology Data Exchange (ETDEWEB)

Lefrancois, M

2005-12-15

In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)

Tunneling time in space fractional quantum mechanics

Science.gov (United States)

Hasan, Mohammad; Mandal, Bhabani Prasad

2018-02-01

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.

A modern approach to quantum mechanics

CERN Document Server

Townsend, John S

2012-01-01

Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend's text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement. Chapters 6 through 10 cover the more traditional subjects in wave mechanics-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subj...

Progress in post-quantum mechanics

Science.gov (United States)

Sarfatti, Jack

2017-05-01

Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.

Integrable multiparametric quantum spin chains

CERN Document Server

Förster, A; Roditi, I; Foerster, Angela; Links, Jon; Roditi, Itzhak

1998-01-01

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.

Pseudo-Hermitian Representation of Quantum Mechanics

International Nuclear Information System (INIS)

Mustafazade, A.

2008-01-01

I will outline a formulation of quantum mechanics in which the inner product on the Hilbert space of a quantum system is treated as a degree of freedom. I will outline some of the basic mathematical and conceptual features of the resulting theory and discuss some of its applications. In particular, I will present a quantum mechanical analogue of Einstein's field equations that links the inner product of the Hilbert space and the Hamiltonian of the system and discuss how the resulting theory can be used to address a variety of problems in classical electrodynamics, relativistic quantum mechanics, and quantum computation

Lectures on quantum mechanics

CERN Document Server

Weinberg, Steven

2013-01-01

Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a concise introduction to modern quantum mechanics. Ideally suited to a one-year graduate course, this textbook is also a useful reference for researchers. Readers are introduced to the subject through a review of the history of quantum mechanics and an account of classic solutions of the Schrödinger equation, before quantum mechanics is developed in a modern Hilbert space approach. The textbook covers many topics not often found in other books on the subject, including alternatives to the Copenhagen interpretation, Bloch waves and band structure, the Wigner–Eckart theorem, magic numbers, isospin symmetry, the Dirac theory of constrained canonical systems, general scattering theory, the optical theorem, the 'in-in' formalism, the Berry phase, Landau levels, entanglement and quantum computing. Problems are included at the ends of chapters, with solutions available for instructors at www.cam...

Quantum Mechanical Earth: Where Orbitals Become Orbits

Science.gov (United States)

Keeports, David

2012-01-01

Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

Quantum mechanics in Hilbert space

CERN Document Server

Prugovecki, Eduard

1981-01-01

A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the

Measurement theory in quantum mechanics

International Nuclear Information System (INIS)

Klein, G.

1980-01-01

It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in a natural way in the quantum mechanics theory. There are no longer fundamental differences between macroscopic and microscopic objects, between classical and quantum objects, between observer and object. Thus, discrepancies and paradoxes have disappeared from the conventional quantum mechanics theory. One consequence of the cumulative memory of the particles is that the sum of negentropy plus information is a constant. Using this theory it is also possible to explain the 'paranormal' phenomena and what is their difference from the 'normal' ones [fr

Emergent quantum mechanics without wavefunctions

International Nuclear Information System (INIS)

Pascasio, J Mesa; Fussy, S; Schwabl, H; Grössing, G

2016-01-01

We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques. (paper)

Randomness and locality in quantum mechanics

International Nuclear Information System (INIS)

Bub, J.

1976-01-01

This paper considers the problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space. The Kochen and Specker theorem proves the impossibility of embedding the possibility structure of a quantum mechanical system into a Boolean algebra. It is shown that a hidden variable theory involves a Boolean representation which is not an embedding, and that such a representation cannot recover the quantum statistics for sequential probabilities without introducing a randomization process for the hidden variables which is assumed to apply only on measurement. It is suggested that the relation of incompatability is to be understood as a type of stochastic independence, and that the indeterminism of a quantum mechanical system is engendered by the existence of independent families of properties. Thus, the statistical relations reflect the possibility structure of the system: the probabilities are logical. The hidden variable thesis is influenced by the Copenhagen interpretation of quantum mechanics, i.e. by some version of the disturbance theory of measurement. Hence, the significance of the representation problem is missed, and the completeness of quantum mechanics is seen to turn on the possibility of recovering the quantum statistics by a hidden variable scheme which satisfies certain physically motivated conditions, such as locality. Bell's proof that no local hidden variable theory can reproduce the statistical relations of quantum mechanics is considered. (Auth.)

Supersymmetric closed string tachyon cosmology: a first approach

International Nuclear Information System (INIS)

Vázquez-Báez, V; Ramírez, C

2014-01-01

We give a worldline supersymmetric formulation for the effective action of closed string tachyon in a FRW background. This is done considering that, as shown by Vafa, the effective theory of closed string tachyons can have worldsheet supersymmetry. The Hamiltonian is constructed by means of the Dirac procedure and written in a quantum version. By using the supersymmetry algebra we are able to find solutions to the Wheeler-DeWitt equation via a more simple set of first order differential equations

On quantum gravity and the many-worlds interpretation of quantum mechanics

International Nuclear Information System (INIS)

Smolin, L.

1984-01-01

The paper examines the interpretation of quantum mechanics and the quantum theory of gravity. Foundational problems in quantum gravity; the many-worlds interpretation of quantum mechanics; the role of observation in the many-worlds and in the minimal relative state interpretations; and advantages of the many-worlds interpretation; are all discussed. (U.K.)

Maximally causal quantum mechanics

International Nuclear Information System (INIS)

Roy, S.M.

1998-01-01

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics. (author)

Non-supersymmetric membrane flows from fake supergravity and multi-trace deformations

International Nuclear Information System (INIS)

Papadimitriou, I.; Hamburg Univ.

2006-06-01

We use fake supergravity as a solution generating technique to obtain a continuum of non-supersymmetric asymptotically AdS 4 x S 7 domain wall solutions of eleven-dimensional supergravity with non-trivial scalars in the SL(8,R)/SO(8) coset. These solutions are continuously connected to the supersymmetric domain walls describing a uniform sector of the Coulomb branch of the M2-brane theory. We also provide a general argument that identifies the fake superpotential with the exact large-N quantum effective potential of the dual theory, thus arriving at a very general description of multi-trace deformations in the AdS/CFT correspondence, which strongly motivates further study of fake supergravity as a solution generating method. This identification allows us to interpret our non-supersymmetric solutions as a family of marginal triple-trace deformations of the Coulomb branch that completely break supersymmetry and to calculate the exact large-N anomalous dimensions of the operators involved. The holographic one- and two-point functions for these solutions are also computed. (Orig.)

Non-supersymmetric membrane flows from fake supergravity and multi-trace deformations

Energy Technology Data Exchange (ETDEWEB)

Papadimitriou, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik

2006-06-15

We use fake supergravity as a solution generating technique to obtain a continuum of non-supersymmetric asymptotically AdS{sub 4} x S{sup 7} domain wall solutions of eleven-dimensional supergravity with non-trivial scalars in the SL(8,R)/SO(8) coset. These solutions are continuously connected to the supersymmetric domain walls describing a uniform sector of the Coulomb branch of the M2-brane theory. We also provide a general argument that identifies the fake superpotential with the exact large-N quantum effective potential of the dual theory, thus arriving at a very general description of multi-trace deformations in the AdS/CFT correspondence, which strongly motivates further study of fake supergravity as a solution generating method. This identification allows us to interpret our non-supersymmetric solutions as a family of marginal triple-trace deformations of the Coulomb branch that completely break supersymmetry and to calculate the exact large-N anomalous dimensions of the operators involved. The holographic one- and two-point functions for these solutions are also computed. (Orig.)

QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

Science.gov (United States)

Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C

2015-08-28

According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion. Copyright © 2015, American Association for the Advancement of Science.

Elementary quantum mechanics

CERN Document Server

Saxon, David S

2012-01-01

Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m

Contact geometry and quantum mechanics

Science.gov (United States)

Herczeg, Gabriel; Waldron, Andrew

2018-06-01

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.

Theoretical physics. Quantum mechanics

International Nuclear Information System (INIS)

Rebhan, Eckhard

2008-01-01

From the first in two comprehensive volumes appeared Theoretical Physics of the author by this after Mechanics and Electrodynamics also Quantum mechanics appears as thinner single volume. First the illustrative approach via wave mechanics is reproduced. The more abstract Hilbert-space formulation introduces the author later by postulates, which are because of the preceding wave mechanics sufficiently plausible. All concepts of quantum mechanics, which contradict often to the intuitive understanding formed by macroscopic experiences, are extensively discussed and made by means of many examples as well as problems - in the largest part provided with solutions - understandable. To the interpretation of quantum mechanics an extensive special chapter is dedicated. this book arose from courses on theoretical physics, which the author has held at the Heinrich-Heine University in Duesseldorf, and was in numerous repetitions fitted to the requirement of the studyings. it is so designed that it is also after the study suited as reference book or for the renewing. All problems are very thoroughly and such extensively studied that each step is separately reproducible. About motivation and good understandability is cared much

Quantum mechanics and computation

International Nuclear Information System (INIS)

Cirac Sasturain, J. I.

2000-01-01

We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs

Lectures on quantum mechanics

International Nuclear Information System (INIS)

Weinberg, Steven

2015-01-01

Quantum mechanics represents the central revolution of modern natural science and reaches in its importance farely beyond physics. Neither chemistry nor biology on the molecular scale would be understandable without it. Modern information technology from the laptop over the mobile telephone and the flat screen until the supercomputer would be unthinkable without quantum-mechanical effects. It desribes the world on the atomic and subatomic scale and is by this the starting point of our modern worldview. The Nobel-prize carrier Steven Weinberg has done ever among others by his theory of the unification of the weak and the electromagnetic interaction one of the most important contributions to this revolution. In this book he reproduces his personal view of quantum mechanics, which captivates by its strictly logic construction, precise linguistic representation, and mathematical clearness and completeness. This book appeals to studyings of natural sciences, especially of physics. Accompanied is the test by exercise problems, which allow the studying to apply immediately the knowledge, but also test their understanding. Because of its precision and clearness ''Lectures on Quantum Mechanics'' by Weinberg is also essentially suited for the self-study.

Supersymmetric gauge theories from string theory

International Nuclear Information System (INIS)

Metzger, St.

2005-12-01

This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G 2 -manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G 2 -manifold is known. Here we construct families of metrics on compact weak G 2 -manifolds, which contain two conical singularities. Weak G 2 -manifolds have properties that are similar to the ones of proper G 2 -manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E 8 x E 8 -heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the classical action. (author)

Supersymmetric quasipotential equations

International Nuclear Information System (INIS)

Zaikov, R.P.

1981-01-01

A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

Study of R-parity Violating Decays of Supersymmetric Particles with the ATLAS Detector at the LHC

CERN Document Server

AUTHOR|(CDS)2101187; Flowerdew, Micheal

Supersymmetry is a space-time symmetry that postulates the existence of new particles. It assigns to each Standard Model fermion (boson) an associated supersymmetric boson (fermion) partner with the same quantum numbers except for spin. The introduction of these new supersymmetric particles provides a potential solution to the hierarchy problem. Discovery of such particles or alternatively an exclusion of a certain supersymmetic parameter space is one of the main purposes of collider experiments. A special scenario of Supersymmetry that enables the decay of the lightest supersymmetric particle to Standard Model particles is studied using proton-proton collision data collected by the ATLAS experiment at center-of-mass energy of 13 TeV. The searched signal is characterized by a final state of at least four leptons, which leads to extraordinarily low background contributions from Standard Model processes. The work described in this thesis assisted to an exclusion of the considered supersymmetric model for hypoth...

The formalisms of quantum mechanics an introduction

CERN Document Server

David, Francois

2015-01-01

These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

International Nuclear Information System (INIS)

Plotnitsky, Arkady

2014-01-01

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well. (paper)

Quantum mechanics

CERN Document Server

Rae, Alastair I M

2007-01-01

PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC

Quantum mechanics & the big world

NARCIS (Netherlands)

Wezel, Jasper van

2007-01-01

Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our

Quantum-mechanical computers and uncomputability

International Nuclear Information System (INIS)

Lloyd, S.

1993-01-01

The time evolution operator for any quantum-mechanical computer is diagonalizable, but to obtain the diagonal decomposition of a program state of the computer is as hard as actually performing the computation corresponding to the program. In particular, if a quantum-mechanical system is capable of universal computation, then the diagonal decomposition of program states is uncomputable. As a result, in a universe in which local variables support universal computation, a quantum-mechanical theory for that universe that supplies its spectrum cannot supply the spectral decomposition of the computational variables. A ''theory of everything'' can be simultaneously correct and fundamentally incomplete

Variational principle in quantum mechanics

International Nuclear Information System (INIS)

Popiez, L.

1986-01-01

The variational principle in a standard, path integral formulation of quantum mechanics (as proposed by Dirac and Feynman) appears only in the context of a classical limit n to 0 and manifests itself through the method of abstract stationary phase. Symbolically it means that a probability amplitude averaged over trajectories denotes a classical evolution operator for points in a configuration space. There exists, however, the formulation of quantum dynamics in which variational priniple is one of basic postulates. It is explained that the translation between stochastic and quantum mechanics in this case can be understood as in Nelson's stochastic mechanics

Quantum mechanics in a nutshell

CERN Document Server

Mahan, Gerald D

2009-01-01

Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original

Recent trials to verify quantum mechanics

International Nuclear Information System (INIS)

Paty, M.

1974-01-01

An account of the experiments which deal with the verification of Quantum Mechanics and the hidden variable problem is made. First, the well-known EPR paradox is recalled which, in spite of its refutation by Bohr, was the starting point of the questionning on the completeness of Quantum Mechanics and of hidden variable theories; and then Bell's theorem, which shows that the two approaches, Quantum Mechanics and hidden variables, can be put in contradiction. Thereafter the various types of experiments which have been carried out on that subject, mostly concerning the correlation measurements between two photons emitted by a quantum system are described. The most recent experimental results are diverging, some of them to confirm and some others to contradict quantum mechanics. A review of these is given; and a discussion is presented about their possible implications [fr

Time in quantum mechanics

CERN Document Server

Mayato, R; Egusquiza, I

2002-01-01

The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.

Stochastic incompleteness of quantum mechanics

International Nuclear Information System (INIS)

Suppes, P.; Zanotti, M.

1976-01-01

This article brings out in as conceptually clear terms as possible what seems to be a major incompleteness in the probability theory of particles offered by classical quantum mechanics. The exact nature of this incompleteness is illustrated by consideration of some simple quantum-mechanical examples. In addition, these examples are contrasted with the fundamental assumptions of Brownian motion in classical physics on the one hand, and with a controversey of a deecade ago in mathematical physchology. The central claim is that clasical quantum mechanics is radically incomplete in its probabilistic account of the motion of particles. In the last part of the article the time-dependent joint distribution of position and momentum of the linear harmonic oscillator is derived, and it is shown how the apparently physically paradoxical statistical independence of position and momentum has a natural explanation. The explanation is given within the framework of the non-quantum-mechanical stochastic theory constructed for such oscillators. (Auth.)

Hilbert space and quantum mechanics

CERN Document Server

Gallone, Franco

2015-01-01

The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...

On low-energy effective action in three-dimensional = 2 and = 4 supersymmetric electrodynamics

Science.gov (United States)

Buchbinder, I. L.; Merzlikin, B. S.; Samsonov, I. B.

2013-11-01

We discuss general structure of low-energy effective actions in = 2 and = 4 three-dimensional supersymmetric electrodynamics (SQED) in gauge superfield sector. There are specific terms in the effective action having no four-dimensional analogs. Some of these terms are responsible for the moduli space metric in the Coulomb branch of the theory. We find two-loop quantum corrections to the moduli space metric in the = 2 SQED and show that in the = 4 SQED the moduli space does not receive two-loop quantum corrections.

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

International Nuclear Information System (INIS)

Yang, C.-D.

2006-01-01

This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schroedinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → p = -ih∇, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov-Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion

From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics

International Nuclear Information System (INIS)

Mugur-Schaechter, M.

1993-01-01

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (states of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a general syntax of relativized conceptualization where any description is explicity and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualiztion. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides towards the answers. Globally the results obtained provide a basis for the future attempts at a general mathematical representation of the processes of conceptualization

Supersymmetric domain walls

NARCIS (Netherlands)

Bergshoeff, Eric A.; Kleinschmidt, Axel; Riccioni, Fabio

2012-01-01

We classify the half-supersymmetric "domain walls," i.e., branes of codimension one, in toroidally compactified IIA/IIB string theory and show to which gauged supergravity theory each of these domain walls belong. We use as input the requirement of supersymmetric Wess-Zumino terms, the properties of

The birth and growth of quantum theory. From quantum hypothesis to quantum mechanics

International Nuclear Information System (INIS)

Peng Huanwu

2001-01-01

The short history covers the birth and early growth of quantum theory from 1900 to 1928, beginning with Planck's formula and the quantum hypothesis for the black-body radiation. After a description of the rise and decline of the old quantum theory in connection with its application in spectroscopy, two paths based on the rigorous formulation of the correspondence principle leading to matrix mechanics (1925) and Dirac's non-commuting q-numbers (1925) are explained. Another path based on the generalization of the wave-particle aspect of light quanta is then shown to lead to wave mechanics (1926). Among the works during the early growth of quantum mechanics in 1927-1928, representation theory, the uncertainty principle, two-electron problems, and Dirac's relativistic theory of electrons are discussed

Moessbauer neutrinos in quantum mechanics and quantum field theory

International Nuclear Information System (INIS)

Kopp, Joachim

2009-01-01

We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Moessbauer neutrino oscillations. First, we compute the combined rate Γ of Moessbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for Γ is identical to the one obtained previously [1] for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Moessbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Moessbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.

Quantum Mechanics as Classical Physics

OpenAIRE

Sebens, CT

2015-01-01

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

Quantum mechanics for applied physics and engineering

CERN Document Server

Fromhold, Albert T

2011-01-01

This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch

Foundations of Quantum Mechanics and Quantum Computation

Science.gov (United States)

Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano

2013-03-01

I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.

Spin analysis of supersymmetric particles

International Nuclear Information System (INIS)

Choi, S.Y.; Martyn, H.U.

2006-12-01

The spin of supersymmetric particles can be determined at e + e - colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles -- smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in e + e - collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza-Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an e + e - collider. (orig.)

Stochastic quantum mechanics and quantum spacetime

International Nuclear Information System (INIS)

Prugovecki, E.

1984-01-01

This monograph deals in part with the physical, mathematical and epistemological reasons behind the failure of past theoretical frameworks, including conventional relativistic quantum mechanics, to bring about a conssistent unification of relativity with quantum theory. The assessment of the past record is set in an historical perspective by citing from original sources, some of which might be partly forgotten or are not that well known, but forcefully illustrate the motivations and goals of the foudners of relativity and quantum theory as they set about developing their respetive disciplines. The proposed framework for unification, which constitutes the bulk of this book, embraces classical as well as quantum theories by implementing an epsitemic idea first put forth by M. Born, namely that all deterministic values for measurable quantitites. The framework gives rise to a whole range of yet unresearched problems, whose solutions are bound to shed some light on the relationship between relativity and quantum theories of the most fundamental physical and mathematical leves. (author). refs.; figs.; tabs

Properties of supersymmetric particles and processes

International Nuclear Information System (INIS)

Barnett, R.M.

1986-01-01

The motivations for experimental searches for supersymmetric particles are discussed. The role of R-parity in these searches is described. The production and decay characteristics of each class of supersymmetric particles are investigated in the context of both e+e- and hadron machines. There is a detailed presentation of a sample calculation of a supersymmetric process. Emphasis is given to the signatures for detection of supersymmetric particles and processes. The current limits for supersymmetric particles are given. 125 refs., 50 figs

Time Asymmetric Quantum Mechanics

Directory of Open Access Journals (Sweden)

Arno R. Bohm

2011-09-01

Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Science Academies' Refresher Course in Quantum Mechanics

Indian Academy of Sciences (India)

IAS Admin

2013-02-28

Feb 28, 2013 ... A Refresher Course in Quantum Mechanics for college/university teachers ... The Course will cover the basic and advanced topics of Quantum ... Module 1:- Principles of Quantum Mechanics (with associated mathematics), ...

Relativistic quantum mechanics; Mecanique quantique relativiste

Energy Technology Data Exchange (ETDEWEB)

Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)

1998-12-01

These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.

Noncommutative quantum mechanics

Science.gov (United States)

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

Quantum gravity

International Nuclear Information System (INIS)

Markov, M.A.; West, P.C.

1984-01-01

This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981

Facets of contextual realism in quantum mechanics

International Nuclear Information System (INIS)

Pan, Alok Kumar; Home, Dipankar

2011-01-01

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

Supersymmetric null-like holographic cosmologies

International Nuclear Information System (INIS)

Lin Fengli; Wen Wenyu

2006-01-01

We construct a new class of 1/4-BPS time dependent domain-wall solutions with null-like metric and dilaton in type II supergravities, which admit a null-like big bang singularity. Based on the domain-wall/QFT correspondence, these solutions are dual to 1/4-supersymmetric quantum field theories living on a boundary cosmological background with time dependent coupling constant and UV cutoff. In particular we evaluate the holographic c function for the 2-dimensional dual field theory living on the corresponding null-like cosmology. We find that this c function runs in accordance with the c-theorem as the boundary universe evolves, this means that the number of degrees of freedom is divergent at big bang and suggests the possible resolution of big bang singularity

QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

International Nuclear Information System (INIS)

Geiger, G.

2000-01-01

The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

Quantum mechanics and stochastic mechanics for compatible observables at different times

International Nuclear Information System (INIS)

Correggi, M.; Morchio, G.

2002-01-01

Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of noninteracting systems at different times

The physics of quantum mechanics

CERN Document Server

Binney, James

2014-01-01

The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be

Instantons and large N an introduction to non-perturbative methods in quantum field theory

CERN Document Server

Marino, Marcos

2015-01-01

This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.

Stochastic mechanics and quantum theory

International Nuclear Information System (INIS)

Goldstein, S.

1987-01-01

Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic) physical reality. Stochastic mechanics presents a unified treatment of the microscopic and macroscopic domains, in which the process of measurement plays no special physical role and which reduces to Newtonian mechanics in the macroscopic limit

Quantum mechanics and precision measurements

International Nuclear Information System (INIS)

Ramsey, N.F.

1995-01-01

The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. Although the Heisenberg Uncertainty Principle often limits measurement accuracies, in many cases the validity of quantum mechanics makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: 1) Existence of discrete quantum states of energy. 2) Energy conservation in transitions between two states. 3) Electromagnetic radiation of frequency v is quantized with energy hv per quantum. 4) The identity principle. 5) The Heisenberg Uncertainty Principle. 6) Addition of probability amplitudes (not probabilities). 7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its effect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems. These effects are discussed and illustrated

Quantum mechanics a modern development

CERN Document Server

Ballentine, Leslie E

2015-01-01

Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...

Mathematical foundation of quantum mechanics

CERN Document Server

Parthasarathy, K R

2005-01-01

This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...

Quantum mechanics in matrix form

CERN Document Server

Ludyk, Günter

2018-01-01

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix  method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

Supersymmetric large extra dimensions and the cosmological constant: an update

International Nuclear Information System (INIS)

Burgess, C.P.

2004-01-01

This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the cosmological constant problem, a short summary of the proposed mechanism is given. The emphasis is on the perspective of the low-energy effective theory in order to see how it addresses the problem of why low-energy particles like the electron do not contribute too large a vacuum energy. This is followed by a discussion of the main objections, which are grouped into the following five topics: (1) Weinberg's No-Go Theorem. (2) Are hidden tunings of the theory required, and are these stable under renormalization? (3) Why should the mechanism apply only now and not rule out possible earlier epochs of inflationary dynamics? (4) How big are quantum effects, and which are the most dangerous? and (5) Even if successful, can the mechanism be consistent with cosmological or current observational constraints? It is argued that there are plausible reasons why the mechanism can thread the potential objections, but that a definitive proof that it does depends on addressing well-defined technical points. These points include identifying what fixes the size of the extra dimensions, checking how topological obstructions renormalize and performing specific calculations of quantum corrections. More detailed studies of these issues, which are well within reach of our present understanding of extra-dimensional theories, are currently underway. As such, the jury remains out concerning the proposal, although the prospects for acquittal still seem good. (An abridged version of this article appears in the proceedings of SUSY 2003.)

Emergence of classical theories from quantum mechanics

International Nuclear Information System (INIS)

Hájícek, P

2012-01-01

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Emergence of quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C

2009-01-01

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

Quantum aspects of black hole entropy

Indian Academy of Sciences (India)

Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black ...

Quantum mechanics selected topics

CERN Document Server

Perelomov, Askold Mikhailovich

1998-01-01

It can serve as a good supplement to any quantum mechanics textbook, filling the gap between standard textbooks and higher-level books on the one hand and journal articles on the other. This book provides a detailed treatment of the scattering theory, multidimensional quasi-classical approximation, non-stationary problems for oscillators and the theory of unstable particles. It will be useful for postgraduate students and researchers who wish to find new, interesting information hidden in the depths of non-relativistic quantum mechanics.

Quantum mechanics and its limits

International Nuclear Information System (INIS)

Lamehi-Rachti, M.; Mittig, W.

1977-01-01

Bell has shown (Bell's inequality) that local hidden variable theories lead to predictions in contradiction with quantum mechanics. This has been tested in low energy proton-proton scattering by the simultaneous measurement of the polarisation of the two protons. The results are in agreement with quantum mechanics and thus in contradiction with the inequality of Bell [fr

A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence

International Nuclear Information System (INIS)

Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge

2004-01-01

The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a 'clock'. Conditional probabilities are computed for variables of the system to take certain values when the 'clock' specifies a certain time. This framework is attractive in contexts where the assumption of usual quantum mechanics of the existence of an external, perfectly classical clock, appears unnatural, as in quantum cosmology. Until recently, there were problems with such constructions in ordinary quantum mechanics with additional difficulties in the context of constrained theories like general relativity. A scheme we recently introduced to consistently discretize general relativity removed such obstacles. Since the clock is now an object subject to quantum fluctuations, the resulting evolution in time is not exactly unitary and pure states decohere into mixed states. Here we work out in detail the type of decoherence generated, and we find it to be of Lindblad type. This is attractive since it implies that one can have loss of coherence without violating the conservation of energy. We apply the framework to a simple cosmological model to illustrate how a quantitative estimate of the effect could be computed. For most quantum systems it appears to be too small to be observed, although certain macroscopic quantum systems could in the future provide a testing ground for experimental observation

Supersymmetric particles at LEP

International Nuclear Information System (INIS)

Barbiellini, G.; Coignet, G.; Gaillard, M.K.; Bonneaud, G.; Ellis, J.; Matteuzzi, C.; Wiik, H.

1979-10-01

The authors examine whether the supersymmetrization of nature at a mass scale up to 100 GeV can be confirmed or excluded by experiments with LEP. They review the qualitative features of the spectroscopy suggested by supersymmetric theories. Then they discuss possible production rates and means of detection of these particles at LEP. In this framework they make some remarks about other projects for future high energy physics machines which can be used for the study of supersymmetric phenomena. (HSI)

Statistical algebraic approach to quantum mechanics

International Nuclear Information System (INIS)

Slavnov, D.A.

2001-01-01

The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

Integrability of a family of quantum field theories related to sigma models

Energy Technology Data Exchange (ETDEWEB)

Ridout, David [Australian National Univ., Canberra, ACT (Australia). Dept. of Theoretical Physics; DESY, Hamburg (Germany). Theory Group; Teschner, Joerg [DESY, Hamburg (Germany). Theory Group

2011-03-15

A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2 vertical stroke 1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS{sub 2} x S{sup 2}, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space. (orig.)

Primer of quantum mechanics

CERN Document Server

Chester, Marvin

2003-01-01

Introductory text examines the classical quantum bead on a track: its state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; and bead in a spherical shell. Also, spin, matrices and structure of quantum mechanics; simplest atom; indistinguishable particles; and stationary-state perturbation theory.

Supersymmetric models without R parity

International Nuclear Information System (INIS)

Ross, G.G.; Valle, J.W.F.

1985-01-01

We show that many supersymmetric models may spontaneously break R parity through scalar neutrinos acquiring a vacuum expectation value (vev). These models allow supersymmetric particles to be produced singly and to decay to nonsupersymmetric states. This leads to a new pattern of supersymmetric phenomenology. We discuss the lepton number violation to be expected in this class of models. (orig.)

Classical- and quantum mechanical Coulomb scattering

International Nuclear Information System (INIS)

Gratzl, W.

1987-01-01

Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)

Undergraduate quantum mechanics: lost opportunities for engaging motivated students?

Science.gov (United States)

Johansson, Anders

2018-03-01

Quantum mechanics is widely recognised as an important and difficult subject, and many studies have been published focusing on students’ conceptual difficulties. However, the sociocultural aspects of studying such an emblematic subject have not been researched to any large extent. This study explores students’ experiences of undergraduate quantum mechanics using qualitative analysis of semi-structured interview data. The results inform discussions about the teaching of quantum mechanics by adding a sociocultural dimension. Students pictured quantum mechanics as an intriguing subject that inspired them to study physics. The study environment they encountered when taking their first quantum mechanics course was however not always as inspiring as expected. Quantum mechanics instruction has commonly focused on the mathematical framework of quantum mechanics, and this kind of teaching was also what the interviewees had experienced. Two ways of handling the encounter with a traditional quantum mechanics course were identified in the interviews; either students accept the practice of studying quantum mechanics in a mathematical, exercise-centred way or they distance themselves from these practices and the subject. The students who responded by distancing themselves experienced a crisis and disappointment, where their experiences did not match the way they imagined themselves engaging with quantum mechanics. The implications of these findings are discussed in relation to efforts to reform the teaching of undergraduate quantum mechanics.

Quantum Mechanics predicts evolutionary biology.

Science.gov (United States)

Torday, J S

2018-07-01

Nowhere are the shortcomings of conventional descriptive biology more evident than in the literature on Quantum Biology. In the on-going effort to apply Quantum Mechanics to evolutionary biology, merging Quantum Mechanics with the fundamentals of evolution as the First Principles of Physiology-namely negentropy, chemiosmosis and homeostasis-offers an authentic opportunity to understand how and why physics constitutes the basic principles of biology. Negentropy and chemiosmosis confer determinism on the unicell, whereas homeostasis constitutes Free Will because it offers a probabilistic range of physiologic set points. Similarly, on this basis several principles of Quantum Mechanics also apply directly to biology. The Pauli Exclusion Principle is both deterministic and probabilistic, whereas non-localization and the Heisenberg Uncertainty Principle are both probabilistic, providing the long-sought after ontologic and causal continuum from physics to biology and evolution as the holistic integration recognized as consciousness for the first time. Copyright © 2018 Elsevier Ltd. All rights reserved.

Teaching Quantum Mechanics on an Introductory Level.

Science.gov (United States)

Muller, Rainer; Wiesner, Hartmut

2002-01-01

Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)

Toy Models of a Nonassociative Quantum Mechanics

International Nuclear Information System (INIS)

Dzhunushaliev, V.

2007-01-01

Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and un observables quantities.

A New Perspective on Relativistic Quantum Mechanics

International Nuclear Information System (INIS)

Kong, Otto C W

2011-01-01

Based on a linear realization formulation of a quantum relativity, - proposed relativity for 'quantum space-time', we introduce the new Poincare-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. While there is supposed to be not separate notion of classical and quantum mechanics at the level of the very unconventional quantum relativity, the Poincare-Snyder relativity is more like a mathematically extended form of Einstein relativity on which we can write down a formal canonical classical and quantum mechanics. We discuss how the Poincare-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and present a first look of the interesting picture from the new perspective.

Chaos. Possible underpinnings for quantum mechanics?

International Nuclear Information System (INIS)

McHarris, Wm.C.

2004-01-01

Alternative, parallel explanations for a number of counter-intuitive concepts connected with the foundations of quantum mechanics can be constructed in terms of nonlinear dynamics. These include ideas as diverse as the statistical exponential decay law and spontaneous symmetry breaking to decoherence itself and the inference from violations of Bell's inequality that local reality is ruled out in hidden variable extensions of quantum mechanics. Such alternative explanations must not be taken as demonstrations of nonlinear underpinnings for quantum mechanics, but they do raise the possibility of their existence. In this article I delve a bit into ideas connected with the exponential decay law and with Bell's inequality as demonstrations. Then an investigation of the Klein-Gordon equation shows that it should not come as a complete surprise that quantum mechanics just might contain fundamental nonlinearities. (author)

Effective equations for the quantum pendulum from momentous quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

2012-08-24

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Elucidating reaction mechanisms on quantum computers

Science.gov (United States)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-01-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011

Elucidating reaction mechanisms on quantum computers

Science.gov (United States)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-07-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Elucidating reaction mechanisms on quantum computers.

Science.gov (United States)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias

2017-07-18

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Quantum mechanics as total physical theory

International Nuclear Information System (INIS)

Slavnov, D.A.

2002-01-01

It is shown that the principles of the total physical theory and conclusions of the standard quantum mechanics are not at such an antagonistic variance as it is usually accepted. The axioms, which make it possible to plot the renewed mathematical scheme of the quantum mechanics are formulated within the frames of the algebraic approach. The above scheme includes the standard mathematical apparatus of the quantum mechanics. Simultaneously there exists the mathematical object, which adequately describes the individual experiment. The examples of applying the proposed scheme is presented [ru

Introduction to quantum statistical mechanics

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Bogolyubov, N.N.

1980-01-01

In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

Quantum mechanics in coherent algebras on phase space

International Nuclear Information System (INIS)

Lesche, B.; Seligman, T.H.

1986-01-01

Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on phase space that fulfills a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from -infinity to +infinity the formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebras allows to apply the formalism to spaces for which the Wigner mapping is not known. Quantum mechanics of a particle in a plane in polar coordinates is discussed as an example. (author)

Supersymmetric extensions of K field theories

Science.gov (United States)

Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.

2012-02-01

We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.

Quantum mechanics. Introduction. 6. rev. and enl. ed.

International Nuclear Information System (INIS)

Greiner, W.

2005-01-01

The following topics are dealt with: Quantization of physical quantities, radiation laws, the wave aspect of matter, mathematical foundations of quantum mechanics, ther Schroedinger equation, the harmonic oscillator, the transition from classical to quantum mechanics, a charged particle in the electromagnetic field, the hydrogen atom, perturbation theory and approximation procedures, spin, a nonrelativistic wave equation with spin, systems of identical particles, the formal scheme of quantum mechanics, conceptions and philosophical problems of quantum mechanics. (HSI)

Testing the foundations of quantum mechanics

CERN Document Server

Gisin, Nicolas; CERN. Geneva

1999-01-01

Quantum mechanics is certainly one of the most fascinating field of physics. In recent years, the new field of "quantum information processing" based on the most fundamental aspect of quantum mechanics, like linearity and entanglement, even increased and its peculiarities. In this series of 4 lectures we shall present some of the issues and experiments that test quantum theory. Entanglement leads, on the one hand side, to the measurement problem, to the EPR paradox and to quantum nonlocality ( distant systems). We will derive the Bell inequality, present experimental results that provide huge evidence in favor of quantum nonlocality and discuss some loopholes that are still open. On the other side, entanglement offers many new possibilities for information processing. Indeed, it provides means to carry out tasks that are either impossible classically (like quantum cryptography and quantum teleportation) or that would require significantly more steps to perform on a classical computer (like searching a databas...

Macroscopic quantum mechanics: theory and experimental concepts of optomechanics

International Nuclear Information System (INIS)

Chen Yanbei

2013-01-01

Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors towards testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this article, I will review a set of techniques of quantum measurement theory that are often used to analyse quantum optomechanical systems. Some of these techniques were originally designed to analyse how a classical driving force passes through a quantum system, and can eventually be detected with an optimal signal-to-noise ratio—while others focus more on the quantum-state evolution of a mechanical object under continuous monitoring. In the second part of this article, I will review a set of experimental concepts that will demonstrate quantum mechanical behaviour of macroscopic objects—quantum entanglement, quantum teleportation and the quantum Zeno effect. Taking the interplay between gravity and quantum mechanics as an example, I will review a set of speculations on how quantum mechanics can be modified for macroscopic objects, and how these speculations—and their generalizations—might be tested by optomechanics. (invited review)

The mechanism of suppression of quantum transitions (quantum whirligig)

International Nuclear Information System (INIS)

Buts, V.A.

2010-01-01

The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time was offered for the excited states, and has received the name as quantum whirligig (QWE). In this work the close connection of the considered mechanism with Zeno effect is shown. The considerations are stated, that many experimental results, which are interpreted as observation of Zeno effect, apparently, correspond to QWE.

Quo Vadis Quantum Mechanics?

CERN Document Server

Dolev, S; Kolenda, N

2005-01-01

For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.

New supersymmetrizations of the generalized KDV hierarchies

International Nuclear Information System (INIS)

Figueroa-O'Farrill, J.M.; Stanciu, S.

1993-03-01

Recently we investigated a new supersymmetrization procedure for the KdV hierarchy inspired in some recent work on supersymmetric matrix models. We extend this procedure here for the generalized KdV hierarchies. The resulting supersymmetric hierarchies are generically nonlocal, expect for the case of Boussinesque which we treat in detail. The resulting supersymmetric hierarchy is integrable and bihamiltonian and contains the Boussinesque hierarchy as a subhierarchy. In a particular realization, we extend it by defining supersymmetric odd flows. We end with some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy. (orig.)

EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

Science.gov (United States)

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the

Advanced quantum mechanics materials and photons

CERN Document Server

Dick, Rainer

2016-01-01

In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of�...

Bethe Ansatz and supersymmetric vacua

International Nuclear Information System (INIS)

Nekrasov, Nikita; Shatashvili, Samson

2009-01-01

Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T 2 . A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.

How to understand quantum mechanics

CERN Document Server

Ralston, John P

2018-01-01

How to Understand Quantum Mechanics presents an accessible introduction to understanding quantum mechanics in a natural and intuitive way, which was advocated by Erwin Schroedinger and Albert Einstein. A theoretical physicist reveals dozens of easy tricks that avoid long calculations, makes complicated things simple, and bypasses the worthless anguish of famous scientists who died in angst. The author's approach is light-hearted, and the book is written to be read without equations, however all relevant equations still appear with explanations as to what they mean. The book entertainingly rejects quantum disinformation, the MKS unit system (obsolete), pompous non-explanations, pompous people, the hoax of the 'uncertainty principle' (it is just a math relation), and the accumulated junk-DNA that got into the quantum operating system by misreporting it. The order of presentation is new and also unique by warning about traps to be avoided, while separating topics such as quantum probability to let the Schroeding...

Mind, matter and quantum mechanics

CERN Document Server

Stapp, Henry P

2009-01-01

"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...

Mathematics and quantum mechanics

International Nuclear Information System (INIS)

Santander, M.

2000-01-01

Several episodes in the relation between Mathematics and Quantum Mechanics are discussed; and the emphasis is put in the existence of multiple and sometimes unexpected connections between ideas originating in Mathematics and in Quantum Physics. The question of the unresasonable effectiveness of Mathematics in Physics is also presented in the same light. (Author) 3 refs

Exploring the boundaries of quantum mechanics: advances in satellite quantum communications.

Science.gov (United States)

Agnesi, Costantino; Vedovato, Francesco; Schiavon, Matteo; Dequal, Daniele; Calderaro, Luca; Tomasin, Marco; Marangon, Davide G; Stanco, Andrea; Luceri, Vincenza; Bianco, Giuseppe; Vallone, Giuseppe; Villoresi, Paolo

2018-07-13

Recent interest in quantum communications has stimulated great technological progress in satellite quantum technologies. These advances have rendered the aforesaid technologies mature enough to support the realization of experiments that test the foundations of quantum theory at unprecedented scales and in the unexplored space environment. Such experiments, in fact, could explore the boundaries of quantum theory and may provide new insights to investigate phenomena where gravity affects quantum objects. Here, we review recent results in satellite quantum communications and discuss possible phenomena that could be observable with current technologies. Furthermore, stressing the fact that space represents an incredible resource to realize new experiments aimed at highlighting some physical effects, we challenge the community to propose new experiments that unveil the interplay between quantum mechanics and gravity that could be realizable in the near future.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Toward a microrealistic version of quantum mechanics. II

International Nuclear Information System (INIS)

Maxwell, N.

1976-01-01

Possible objections to the propensity microrealistic version of quantum mechanics proposed previously are answered. This version of quantum mechanics is compared with the statistical, particle, microrealistic viewpoint, and a crucial experiment is proposed designed to distinguish between these two microrealistic versions of quantum mechanics

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

International Nuclear Information System (INIS)

Schulze-Halberg, Axel; Wang, Jie

2015-01-01

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system

Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners

Energy Technology Data Exchange (ETDEWEB)

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: wangjie@iun.edu [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2015-07-15

We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.

Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact.

Science.gov (United States)

Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

2018-01-12

Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from 'electrochemical' to 'mechanical', which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.

Nonlocality and localizability in quantum mechanics

International Nuclear Information System (INIS)

Matsuno, K.

1989-01-01

Nonlocality of simultaneous spatial correlation of a quantum phenomenon as demonstrated in various versions of Einstein-Podolsky-Rosen type experiment reduces to nonlocality of the measurement apparatus in the sense that the eigen-wavefunctions for the apparatus are completely specified in a manner of being independent of whatever object it may measure. Nonlocality of the measurement apparatus however serves as no more than a good approximation to reality at best. The theoretical imposition of nonlocality of the measurement apparatus as an approximation is compatible with the actual locality of quantum mechanics that dispenses with an agent claiming globally simultaneous specifiability of boundary conditions, though the genuine locality of quantum mechanics has to be examined without employing the nonlocality of the measurement apparatus. The actual locality of quantum mechanics is intrinsically irreversible in its development

Introduction to quantum mechanics a time-dependent perspective

CERN Document Server

Tannor, David J

2007-01-01

"Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.

Lectures in quantum mechanics a two-term course

CERN Document Server

Picasso, Luigi E

2016-01-01

Based on a series of university lectures on nonrelativistic quantum mechanics, this textbook covers a wide range of topics, from the birth of quantum mechanics to the fine-structure levels of heavy atoms. The author sets out from the crisis in classical physics and explores the seminal ideas of Einstein, Bohr, and de Broglie and their vital importance for the development of quantum mechanics. There follows a bottom-up presentation of the postulates of quantum mechanics through real experiments (such as those of neutron interferometry), with consideration of their most important consequences, including applications in the field of atomic physics. A final chapter is devoted to the paradoxes of quantum mechanics, and particularly those aspects that are still open and hotly debated, to end up with a mention to Bell's theorem and Aspect's experiments. In presenting the principles of quantum mechanics in an inductive way, this book has already proved very popular with students in its Italian language version.It c...

Quantum mechanics a comprehensive text for chemistry

CERN Document Server

Arora, Kishor

2010-01-01

This book contains 14 chapters. The text includes the inadequacy of classical mechanics and covers basic and fundamental concepts of quantum mechanics including concepts of transitional, vibration rotation and electronic energies, introduction to concepts of angular momenta, approximatemethods and their application concepts related to electron spin, symmetery concepts and quantum mechanics and ultimately the book features the theories of chemical bonding and use of softwares in quantum mechanics. the text of the book is presented in a lucid manner with ample examples and illustrations wherever

The transactional interpretation of quantum mechanics

Science.gov (United States)

Cramer, John G.

2001-06-01

The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)

2010-11-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

International Nuclear Information System (INIS)

Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco

2010-01-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

The quantum mechanics solver. How to apply quantum theory to modern physics. 2. ed.

International Nuclear Information System (INIS)

Basdevant, J.L.; Dalibard, J.

2006-01-01

The Quantum Mechanics Solver uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics. All of these problems are based on actual physical examples, even if sometimes the mathematical structure of the models under consideration is simplified intentionally in order to get hold of the physics more rapidly. The new edition features new themes, such as the progress in measuring neutrino oscillations, quantum boxes, the quantum thermometer etc. Secondly, it includes a brief summary on the basics of quantum mechanics and the formalism we use. Finally, the problems under three main themes: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. (orig.)

Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics

International Nuclear Information System (INIS)

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2006-01-01

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared--it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification - a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10 -7 calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity

The equivalence principle in classical mechanics and quantum mechanics

OpenAIRE

Mannheim, Philip D.

1998-01-01

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.

Cartoon computation: quantum-like computing without quantum mechanics

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek

2007-01-01

We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed-they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpretation and allows for a cartoon representation. (fast track communication)

A 'general boundary' formulation for quantum mechanics and quantum gravity

International Nuclear Information System (INIS)

Oeckl, Robert

2003-01-01

I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such 'general boundary' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a 'general boundary' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three-dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four-dimensional quantum gravity

The grin of Cheshire cat resurgence from supersymmetric localization

Directory of Open Access Journals (Sweden)

Daniele Dorigoni, Philip Glass

2018-02-01

Full Text Available First we compute the $\\mbox{S}^2$ partition function of the supersymmetric $\\mathbb{CP}^{N-1}$ model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the $\\mathbb{CP}^1$ case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instanton-anti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from $N$ to $r\\in\\mathbb{R}$. Although for generic real $r$ supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer $r$ to recover the undeformed model.

Extracontextuality and extravalence in quantum mechanics.

Science.gov (United States)

Auffèves, Alexia; Grangier, Philippe

2018-07-13

We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Entropy, Topological Theories and Emergent Quantum Mechanics

Directory of Open Access Journals (Sweden)

D. Cabrera

2017-02-01

Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.

Mathematical concepts of quantum mechanics. 2. ed.

International Nuclear Information System (INIS)

Gustafson, Stephen J.; Sigal, Israel Michael

2011-01-01

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)

Theoretical and quantum mechanics fundamentals for chemists

CERN Document Server

Ivanov, Stefan

2006-01-01

Provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between themUniquely presented to be used for self-taught courses covering theoretical and quantum mechanicsEach chapter includes a detailed outline, a summary, self-assessment questions for which answers can be found in the textInvaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics.

Communication: Quantum mechanics without wavefunctions

Energy Technology Data Exchange (ETDEWEB)

Schiff, Jeremy [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Poirier, Bill [Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061 (United States) and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051 (United States)

2012-01-21

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

Communication: Quantum mechanics without wavefunctions

International Nuclear Information System (INIS)

Schiff, Jeremy; Poirier, Bill

2012-01-01

We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

Lectures on Quantum Mechanics

Science.gov (United States)

Weinberg, Steven

2015-09-01

Preface; Notation; 1. Historical introduction; 2. Particle states in a central potential; 3. General principles of quantum mechanics; 4. Spin; 5. Approximations for energy eigenstates; 6. Approximations for time-dependent problems; 7. Potential scattering; 8. General scattering theory; 9. The canonical formalism; 10. Charged particles in electromagnetic fields; 11. The quantum theory of radiation; 12. Entanglement; Author index; Subject index.

Theoretical physics 3. Quantum mechanics 1 with problems in MAPLE

International Nuclear Information System (INIS)

Reineker, P.; Schulz, M.; Schulz, B.M.

2007-01-01

The following topics are dealt with: Historically heuristic introduction to quantum mechanics, the Schroedinger equation, foundations of quantum mechanics, the linear harmonic oscillator, quantum-mechanical motion in the central field, approximation methods for the solution of quantum mechanical problems, motion of particles in the electromagnetic field, spin and magnetic moment of the electron, many-particle systems, conceptional problems of quantum mechanics

Stochastic methods in quantum mechanics

CERN Document Server

Gudder, Stanley P

2005-01-01

Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

Energy Technology Data Exchange (ETDEWEB)

Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl

2017-02-15

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

International Nuclear Information System (INIS)

Plyushchay, Mikhail S.

2017-01-01

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

Likelihood analysis of supersymmetric SU(5) GUTs

Energy Technology Data Exchange (ETDEWEB)

Bagnaschi, E.; Weiglein, G. [DESY, Hamburg (Germany); Costa, J.C.; Buchmueller, O.; Citron, M.; Richards, A.; De Vries, K.J. [Imperial College, High Energy Physics Group, Blackett Laboratory, London (United Kingdom); Sakurai, K. [University of Durham, Science Laboratories, Department of Physics, Institute for Particle Physics Phenomenology, Durham (United Kingdom); University of Warsaw, Faculty of Physics, Institute of Theoretical Physics, Warsaw (Poland); Borsato, M.; Chobanova, V.; Lucio, M.; Martinez Santos, D. [Universidade de Santiago de Compostela, Santiago de Compostela (Spain); Cavanaugh, R. [Fermi National Accelerator Laboratory, Batavia, IL (United States); University of Illinois at Chicago, Physics Department, Chicago, IL (United States); Roeck, A. de [CERN, Experimental Physics Department, Geneva (Switzerland); Antwerp University, Wilrijk (Belgium); Dolan, M.J. [University of Melbourne, ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, Parkville (Australia); Ellis, J.R. [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Theoretical Physics Department, CERN, Geneva 23 (Switzerland); Flaecher, H. [University of Bristol, H.H. Wills Physics Laboratory, Bristol (United Kingdom); Heinemeyer, S. [Campus of International Excellence UAM+CSIC, Cantoblanco, Madrid (Spain); Instituto de Fisica Teorica UAM-CSIC, Madrid (Spain); Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain); Isidori, G. [Universitaet Zuerich, Physik-Institut, Zurich (Switzerland); Olive, K.A. [University of Minnesota, William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, Minneapolis, MN (United States)

2017-02-15

We perform a likelihood analysis of the constraints from accelerator experiments and astrophysical observations on supersymmetric (SUSY) models with SU(5) boundary conditions on soft SUSY-breaking parameters at the GUT scale. The parameter space of the models studied has seven parameters: a universal gaugino mass m{sub 1/2}, distinct masses for the scalar partners of matter fermions in five- and ten-dimensional representations of SU(5), m{sub 5} and m{sub 10}, and for the 5 and anti 5 Higgs representations m{sub H{sub u}} and m{sub H{sub d}}, a universal trilinear soft SUSY-breaking parameter A{sub 0}, and the ratio of Higgs vevs tan β. In addition to previous constraints from direct sparticle searches, low-energy and flavour observables, we incorporate constraints based on preliminary results from 13 TeV LHC searches for jets + E{sub T} events and long-lived particles, as well as the latest PandaX-II and LUX searches for direct Dark Matter detection. In addition to previously identified mechanisms for bringing the supersymmetric relic density into the range allowed by cosmology, we identify a novel u{sub R}/c{sub R} - χ{sup 0}{sub 1} coannihilation mechanism that appears in the supersymmetric SU(5) GUT model and discuss the role of ν{sub τ} coannihilation. We find complementarity between the prospects for direct Dark Matter detection and SUSY searches at the LHC. (orig.)

Likelihood analysis of supersymmetric SU(5) GUTs

Energy Technology Data Exchange (ETDEWEB)

Bagnaschi, E. [DESY, Hamburg (Germany); Costa, J.C. [Imperial College, London (United Kingdom). Blackett Lab.; Sakurai, K. [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomonology; Warsaw Univ. (Poland). Inst. of Theoretical Physics; Collaboration: MasterCode Collaboration; and others

2016-10-15

We perform a likelihood analysis of the constraints from accelerator experiments and astrophysical observations on supersymmetric (SUSY) models with SU(5) boundary conditions on soft SUSY-breaking parameters at the GUT scale. The parameter space of the models studied has 7 parameters: a universal gaugino mass m{sub 1/2}, distinct masses for the scalar partners of matter fermions in five- and ten-dimensional representations of SU(5), m{sub 5} and m{sub 10}, and for the 5 and anti 5 Higgs representations m{sub H{sub u}} and m{sub H{sub d}}, a universal trilinear soft SUSY-breaking parameter A{sub 0}, and the ratio of Higgs vevs tan β. In addition to previous constraints from direct sparticle searches, low-energy and avour observables, we incorporate constraints based on preliminary results from 13 TeV LHC searches for jets+E{sub T} events and long-lived particles, as well as the latest PandaX-II and LUX searches for direct Dark Matter detection. In addition to previously-identified mechanisms for bringing the supersymmetric relic density into the range allowed by cosmology, we identify a novel u{sub R}/c{sub R}-χ{sup 0}{sub 1} coannihilation mechanism that appears in the supersymmetric SU(5) GUT model and discuss the role of ν{sub T} coannihilation. We find complementarity between the prospects for direct Dark Matter detection and SUSY searches at the LHC.

Quantum mechanics and dynamics in phase space

International Nuclear Information System (INIS)

Zlatev, I.S.

1979-01-01

Attention is paid to formal similarity of quantum mechanics and classical statistical physics. It is supposed that quantum mechanics can be reformulated by means of the quasiprobabilistic distributions (QPD). The procedure of finding a possible dynamics of representative points in a phase space is described. This procedure would lead to an equation of the Liouville type for the given QPD. It is shown that there is always a dynamics for which the phase volume is preserved and there is another dynamics for which the equations of motion are ''canonical''. It follows from the paper that in terms of the QPD the quantum mechanics is analogous to the classical statistical mechanics and it can be interpreted as statistics of phase points, their motion obeying the canonical equations. The difference consists in the fact that in the classical statistical physics constructed is statistics of points in a phase space which depict real, existing, observable states of the system under consideration. In the quantum mechanics constructed is statistics of points in a phase space which correspond to the ''substrate'' of quantum-mechanical objects which have no any physical sense and cannot be observed separately

Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons

Energy Technology Data Exchange (ETDEWEB)

Braathen, Johannes; Goodsell, Mark D. [LPTHE, UPMC Univ. Paris 6, Sorbonne Universites, Paris (France); LPTHE, CNRS, Paris (France); Staub, Florian [Karlsruhe Institute of Technology, Institute for Theoretical Physics (ITP), Karlsruhe (Germany); Karlsruhe Institute of Technology, Institute for Nuclear Physics (IKP), Eggenstein-Leopoldshafen (Germany)

2017-11-15

The calculation of the Higgs mass in general renormalisable field theories has been plagued by the so-called ''Goldstone Boson Catastrophe'', where light (would-be) Goldstone bosons give infra-red divergent loop integrals. In supersymmetric models, previous approaches included a workaround that ameliorated the problem for most, but not all, parameter space regions; while giving divergent results everywhere for non-supersymmetric models. We present an implementation of a general solution to the problem in the public code SARAH, along with new calculations of some necessary loop integrals and generic expressions. We discuss the validation of our code in the Standard Model, where we find remarkable agreement with the known results. We then show new applications in Split SUSY, the NMSSM, the Two-Higgs-Doublet Model, and the Georgi-Machacek model. In particular, we take some first steps to exploring where the habit of using tree-level mass relations in non-supersymmetric models breaks down, and show that the loop corrections usually become very large well before naive perturbativity bounds are reached. (orig.)

Toward precision holography with supersymmetric Wilson loops

Energy Technology Data Exchange (ETDEWEB)

Faraggi, Alberto [Instituto de Física, Pontificia Universidad Católica de Chile,Casilla 306, Santiago (Chile); Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Department of Physics,University of Michigan, Ann Arbor, MI 48109 (United States); Silva, Guillermo A. [Instituto de Física de La Plata - CONICET & Departamento de Física - UNLP,C.C. 67, 1900 La Plata (Argentina); Trancanelli, Diego [Institute of Physics, University of São Paulo,05314-970 São Paulo (Brazil)

2016-04-11

We consider certain 1/4 BPS Wilson loop operators in SU(N)N=4 supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS{sub 5}×S{sup 5}. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.

Probable Inference and Quantum Mechanics

International Nuclear Information System (INIS)

Grandy, W. T. Jr.

2009-01-01

In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

The cellular automaton interpretation of quantum mechanics

CERN Document Server

't Hooft, Gerard

2016-01-01

This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...

Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction

International Nuclear Information System (INIS)

Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.

2004-01-01

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a time-independent observable in PT-symmetric quantum field theory

Collisional processes in supersymmetric plasma

International Nuclear Information System (INIS)

Czajka, Alina; Mrowczynski, Stanislaw

2011-01-01

Collisional processes in ultrarelativistic N=1 supersymmetric QED plasma are studied and compared to those in an electromagnetic plasma of electrons, positrons and photons. Cross sections of all binary interactions which occur in the supersymmetric plasma at the order of e 4 are computed. Some processes, in particular, the Compton scattering on selectrons, appear to be independent of momentum transfer and thus they are qualitatively different from processes in an electromagnetic plasma. It suggests that the transport properties of the supersymmetric plasma are different than those of its nonsupersymmetric counterpart. Energy loss and momentum broadening of a particle traversing the supersymmetric plasma are discussed in detail and the characteristics are shown to be surprisingly similar to those of QED plasma.

Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic

Science.gov (United States)

Resconi, Germano; Klir, George J.; Pessa, Eliano

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

Pseudospectra in non-Hermitian quantum mechanics

Science.gov (United States)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

On quantum mechanics for macroscopic systems

International Nuclear Information System (INIS)

Primas, H.

1992-01-01

The parable of Schroedinger's cat may lead to several up-to date questions: how to treat open systems in quantum theory, how to treat thermodynamically irreversible processes in the quantum mechanics framework, how to explain, following the quantum theory, the existence, phenomenologically evident, of classical observables, what implies the predicted existence by the quantum theory of non localized macroscopic material object ?

New progress of fundamental aspects in quantum mechanics

International Nuclear Information System (INIS)

Sun Changpu

2001-01-01

The review recalls the conceptual origins of various interpretations of quantum mechanics. With the focus on quantum measurement problems, new developments of fundamental quantum theory are described in association with recent experiments such as the decoherence process in cavity quantum electrodynamics 'which-way' detection using the Bragg scattering of cold atoms, and quantum interference using the small quantum system of molecular C 60 . The fundamental problems include the quantum coherence of a macroscopic object, the von Neumann chain in quantum measurement, the Schroedinger cat paradox, et al. Many land math experiments have been accomplished with possible important applications in quantum information. The most recent research on the new quantum theory by G.'t Hooft is reviewed, as well as future prospects of quantum mechanics

Quantum Backaction Evading Measurement of Collective Mechanical Modes.

Science.gov (United States)

Ockeloen-Korppi, C F; Damskägg, E; Pirkkalainen, J-M; Clerk, A A; Woolley, M J; Sillanpää, M A

2016-09-30

The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.

Testing quantum mechanics using third-order correlations

International Nuclear Information System (INIS)

Kinsler, P.

1996-01-01

Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of open-quote open-quote semiclassical theories,close-quote close-quote and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the open-quote open-quote all or nothing close-quote close-quote Greenberger-Horne-Zeilinger test of local hidden variable theories. copyright 1996 The American Physical Society

On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

International Nuclear Information System (INIS)

Lee, Sang-Bong.

1993-09-01

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover's and Kubo-Fox-Keizer's approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty

Coherent states in quantum mechanics

CERN Document Server

Rodrigues, R D L; Fernandes, D

2001-01-01

We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.

Polymer quantum mechanics and its continuum limit

International Nuclear Information System (INIS)

Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.

2007-01-01

A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model

Decoherence in quantum mechanics and quantum cosmology

Science.gov (United States)

Hartle, James B.

1992-01-01

A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

''Topological'' (Chern-Simons) quantum mechanics

International Nuclear Information System (INIS)

Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.

1990-01-01

We construct quantum-mechanical models that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and we study the phase-space reductive limiting procedure that takes the former to the latter. The zero-point spectra of operators behave discontinuously in the limit, as a consequence of a nonperturbative quantum-mechanical anomaly. The nature of the limit for wave functions depends on the representation, but is always such that normalization is preserved

Phase space quantum mechanics and maximal acceleration

International Nuclear Information System (INIS)

Caianiello, E.

1989-01-01

My presentation is a synopsis of work done since 1979 in search of connections among information theory, systems theory, quantum mechanics and other matters. The aim was 'to extract geometry from quantum mechanics'. (orig./HSI)

Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.

Science.gov (United States)

Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori

2016-10-11

The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantum mechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an S N 1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantum mechanical interaction with CMP.

Zeno dynamics in quantum statistical mechanics

International Nuclear Information System (INIS)

Schmidt, Andreas U

2003-01-01

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium

Physics: quantum mechanics

International Nuclear Information System (INIS)

Basdevant, J.L.

1983-01-01

This book is the second part of the physic lectures on quantum mechanics from Ecole Polytechnique. It contains some physic complements a little more thoroughly studied, mathematical complements to which refer, and an exercise and problem collection [fr

Axiomation of quantum mechanics

International Nuclear Information System (INIS)

Kotecky, R.

1975-01-01

Deeper understanding of the basic structure of the formalism of the modern quantum theory (as has been established during its 50 years' stormy development) has been brought about by its axiomatization - by founding the formalism merely on experimentally directly accountable postulates without referring to historical development, without any a priori nonessential or empirically nonexplicable assumptions. A summary is given of the common formalism of quantum mechanics and its most significant axiomatizations. The assumptions are discussed under which respective axiomatically described abstract structures may be modelled by means of the common formalisn of quantum theory (established on the theory of Hilbert spaces). (author)

Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact

Science.gov (United States)

Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

2018-01-01

Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from ‘electrochemical’ to ‘mechanical’, which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.

Entanglement, information, and the interpretation of quantum mechanics

International Nuclear Information System (INIS)

Jaeger, Gregg

2009-01-01

This book explores the nature of quantum entanglement and quantum information and their role in the quantum world. Their relations to a number of key experiments and thought experiments in the history of quantum physics are considered, as is a range of interpretations of quantum mechanics that have been put forward as a means of understanding the fundamental nature of microphysics - the traditionally accepted domain of quantum mechanics - and in some cases, the universe as a whole. In this way, the book reveals the deep significance of entanglement and quantum information for our understanding of the physical world. (orig.)

Bell trajectories for revealing quantum control mechanisms

International Nuclear Information System (INIS)

Dennis, Eric; Rabitz, Herschel

2003-01-01

The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ''beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model seven-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise

Path Integrals in Quantum Mechanics

International Nuclear Information System (INIS)

Chetouani, L

2005-01-01

By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics. What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully. The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further. (book review)

Quantum mechanics and the science of measurements

International Nuclear Information System (INIS)

Ramsey, N.F.

1992-01-01

The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10,000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. In popular accounts of quantum mechanics, such great emphases is placed on the Heisenberg Uncertainty Principle that it often appears that the primary effect of quantum mechanics should be to diminish measurement accuracy whereas in most cases it is the validity of quantum mechanics that makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: (1) Existence of discrete quantum states of energy W i . (2) Energy conservation in transitions between two states. (3) Electromagnetic radiation of frequency ν is quantized with energy hν per quantum. (4) The identity principle. (5) The Heisenberg Uncertainty Principle. (6) Addition of probability amplitudes (not probabilities) so P=vertical strokeψ 1 +ψ 2 vertical stroke 2 ≠vertical strokeψ 1 vertical stroke 2 +vertical strokeψ 2 vertical stroke 2 . (7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its affect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems and the identity principle provides meaning and significance to highly precise measurements with quantized systems. These effects are discussed and illustrated. (orig.)

Duality in supersymmetric Yang-Mills theory

International Nuclear Information System (INIS)

Peskin, M.E.

1997-02-01

These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N f c , in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs

Supersymmetric grand unified theories from quarks to strings via SUSY GUTs

CERN Document Server

Raby, Stuart

2017-01-01

These course-tested lectures provide a technical introduction to Supersymmetric Grand Unified Theories (SUSY GUTs), as well as a personal view on the topic by one of the pioneers in the field. While the Standard Model of Particle Physics is incredibly successful in describing the known universe it is, nevertheless, an incomplete theory with many free parameters and open issues. An elegant solution to all of these quandaries is the proposed theory of SUSY GUTs. In a GUT, quarks and leptons are related in a simple way by the unifying symmetry and their electric charges are quantized, further the relative strength of the strong, weak and electromagnetic forces are predicted. SUSY GUTs additionally provide a framework for understanding particle masses and offer candidates for dark matter. Finally, with the extension of SUSY GUTs to string theory, a quantum-mechanically consistent unification of the four known forces (including gravity) is obtained. The book is organized in three sections: the first section contai...

New developments in quantum mechanics

CERN Document Server

Aharonov, Yakir

1994-01-01

After a general introduction, some new developments on the more subtle predictions of Quantum Mechanics and their interpretation will be discussed. These include non-local topological effects, physics of pre- and post-selected quantum systems, and the question of observability of the Schrödinger wave itself.

Coherent states in quantum mechanics

International Nuclear Information System (INIS)

Rodrigues, R. de Lima; Fernandes Junior, Damasio; Batista, Sheyla Marques

2001-12-01

We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out. (author)

Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory

Science.gov (United States)

Plotnitsky, Arkady

2015-10-01

These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.

Relationship between quantum walks and relativistic quantum mechanics

International Nuclear Information System (INIS)

Chandrashekar, C. M.; Banerjee, Subhashish; Srikanth, R.

2010-01-01

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

Quantum mechanical streamlines. I - Square potential barrier

Science.gov (United States)

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Relativistic quantum mechanics of leptons and fields

International Nuclear Information System (INIS)

Grandy, W.T. Jr.

1991-01-01

This book serves as an advanced text on the Dirac theory, and provides a monograph summarizing the description of relativistic quantum mechanics and quantum electrodynamics as classical field theories. It presents a broad, detailed, and up-to-date exposition of relativistic quantum mechanics, including the two-body problem. It also demonstrates the extent to which the behavior of stable particles and their interactions can be understood without introducing operator (second-quantized) fields. The subsequent difficulties are studied in detail and possible resolutions are presented through quantum field theory

Optimization of a relativistic quantum mechanical engine.

Science.gov (United States)

Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

2016-08-01

We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

Advanced quantum mechanics materials and photons

CERN Document Server

Dick, Rainer

2012-01-01

Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquir...

Supersymmetry in the Majorana Cooper-pair box

NARCIS (Netherlands)

Ulrich, Jascha; Adagideli, Inanc; Schuricht, Dirk; Hassler, Fabian

2014-01-01

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high-energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the

Recent developments in quantum mechanics

International Nuclear Information System (INIS)

Piron, C.

1989-01-01

It is essentially a review of recent progress in Quantum Mechanics obtained by the ''Geneva School'', put all together in a synthesis for the first time. During these twelve last years Quantum Mechanics has developed deeply in three aspects: 1) the interpretation has been completely clarified but many ''senior'' physicists delight in the mystery of their school-days Quantum Mechanics and do not want to change their minds. 2) The formalism has been developed and generalized to many (if it is not all) physical situations. 3) Many new rules of calculation have been developed. In conclusion many paradoxes and/or unsolved problems have been solved and many calculations which usually appear just as tricks can be explained and justified. I want here to give a brief survey of each one of these three points and to end by some examples which show the power and the efficiency of this new theory. (orig.)

The massless limit of supersymmetric QCD

International Nuclear Information System (INIS)

Davis, A.C.; Dine, M.; Seiberg, N.

1983-01-01

We construct an effective lagrangian for supersymmetric QCD, using a simple set of rules. The model with non-zero quark mass, msub(q), has at least N supersymmetric vacua, where N is the number of colors (in agreement with Witten's index). These vacua move to infinity as msub(q)->0. We study the possibility of supersymmetric breaking at msub(q)=0. (orig.)

Fundamentals of quantum mechanics

CERN Document Server

Erkoc, Sakir