DOCSLIB.ORG

A Vortex Formulation of Quantum Physics Setting Discrete Quantum States Into Continuous Space-Time

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Vortex Formulation of Quantum Physics Setting Discrete Quantum States Into Continuous Space-Time Fred Y. Ye, IJNSR, 2017; 1:4 Research Article IJNSR (2017) 1:4 International Journal of Natural Science and Reviews (ISSN:2576-5086) A Vortex Formulation of Quantum Physics Setting Discrete Quantum States into Continuous Space-time Fred Y. Ye 1, 2* 1 School of Information Management, Nanjing University, Nanjing 210023, CHINA 2International Joint Informatics Laboratory (IJIL), UI-NU, Champaign-Nanjing ABSTRACT Any quantum state can be described by a vortex, which is math- *Correspondence to Author: ematically a multi-vector and physically a united-measure. Fred Y. Ye When the vortex formulation of quantum physics is introduced, School of Information Management, Hamil-ton principle keeps its core position in physical analysis. Nanjing University, Nanjing 210023, While the global characteristics are described by Lagranrian CHINA; International Joint Informat- function for dynamics and double complex core function for ics Laboratory (IJIL), UI-NU, Cham- stable states, Schrödinger equation and gauge symmetries paign-Nanjing reveal local char-acteristics. The vortex-based physics provides a new unified understanding of wave-particle duality and uncertainty, quantum entanglement and teleportation, as How to cite this article: well as quantum information and computation, with setting Fred Y. Ye. A Vortex Formulation of discrete quantum states into con-tinuous space-time for Quantum Physics Setting Discrete keeping concordance of methodology in processing micro- Quantum States into Continuous particle and macro-galaxy. Two fundamental experiments are Space-time. International Journal suggested to correct and verify the physical for-mulation. of Natural Science and Reviews, 2017; 1:4. Keywords: Vortex; vortex formulation; quantum mechanism; quantum state; quantum physics; space-time eSciPub LLC, Houston, TX USA. Website: http://escipub.com/ http://escipub.com/international-journal-of-natural-science-and-reviews/ 0001 Fred Y. Ye, IJNSR, 2017; 1:4 INTRODUCTION The path integral formulation of quantum There are a few famous formulations of mechanics is a description of quantum theory quantum physics, in which we mention three that generalizes the action principle of classical [4] main representative formulations: Schrödinger mechanics . It replaces the classical notion of wave formulation, Heisenberg matrix a single, unique classical trajectory for a system formulation and Feynman path integral with a sum, or functional integral, over an infinity formulation [1]. of quantum-mechanically possible trajectories to compute a quantum amplitude. This In wave formulation, the state of a system at a formulation has proven crucial to the given time is described by a complex wave subsequent development of theoretical physics, function, also referred to as state vector in a because manifest Lorentz covariance (time and complex vector space. The Schrödinger space components of quantities enter equations equation describes how wave functions change in the same way) is easier to achieve than in the in time. In the formulation, the operators stay operator formalism of canonical quantization. fixed while the Schrödinger equation changes Unlike previous methods, the path integral the basis with time. However, the wave packet allows a physicist to easily change coordinates will also spread out as time progresses, which between very different canonical descriptions of means that the position becomes more the same quantum system. Another advantage uncertain with time. This also has the effect of is that it is in practice easier to guess the correct turning a position eigenstate, which can be form of the Lagrangian of a theory, which thought of as an infinitely sharp wave packet, naturally enters the path integrals, than the into a broadened wave packet that no longer Hamiltonian. represents a definite position eigenstate [2]. In this paper, a vortex formulation is suggested, In matrix formulation, it is the operators which and the bracket notations are including three change in time while the basis of the space main types as follows. remains fixed. A fixed basis is, in some ways, more mathematically pleasing. This formulation (1) Dirac bra–ket notation < | and | >: the left also generalizes more easily to relativity. Matrix part < |, called “bra”, represents a row vector, mechanics was the first conceptually while the right part | >, called “ket”, denotes a autonomous and logically consistent formulation column vector; and < | > represents an inner of quantum physics. product, producing a scalar, while the | > < | denotes an outer product, producing a tensor. Dirac’s interaction gave a link of matrix formulation and wave formulation, via manifest (2) Commutated notation: It is defined that [X, Y] in Dirac's bra–ket notation [3], where matrix = XY – YX for measures X and Y. Mostly, [X, Y] formulation and wave formulation are ≠ [Y, X]. Particularly, following non-commutation equivalence of both the basis and the operators, relation contributes quantum mechanism carrying time-dependence. The interaction [X ,Y] XY YX i (1) picture allows for operators to act on the state vector at different times and forms the basis for in which i is the imaginary unit and ℏ is the quantum field theory and other methods. reduced Planck's constant (ℏ =h/2π). http://escipub.com/international-journal-of-natural-science-and-reviews/ 0002 Fred Y. Ye, IJNSR, 2017; 1:4 (3) Poisson bracket notation { }: It is defined that The covariant derivative and the differential operators of two order derivatives are defined {f, g} = = -{g, f} for functions f and g. respectively as The differential operators of one order 2 derivatives are defined as D ( ) ; g ; g (7) where we see that space-time metric g is ; (2) x naturally generated. In the paper, we use Greek in which four Dirac matrices are viewed as four subscripts μ, ν to denote 1, 2, 3, 4 and Latin orthonormal basis vectors for real space-time subscripts i, j to do 1, 2, 3. This is a foundational mathematical framework of physics. I 0 0 k Now we introduce some new ideas to 0 , k (3) k 0 I 0 understand quantum states via vortex, which can visually combine point particle, wave vector where 0 is time-like vector and and spin together, for setting discrete quantum states into continuous space-time. k (k 1,2,3) space-like vectors. Similarly, the three Pauli matrices k ( 1, 2 , 3 ) are THEORETICAL FOUNDATIONS: Vortex- based physics viewed as three orthonormal basis vectors for three dimensional Euclidean space A vortex is mathematically represented by a multi-vector, and physically describes linked-measure [7-9], which contributes a new 1 0 1 2 0 i 3 1 0 math-physical methodology to understand , , (4) 1 0 i 0 0 1 physical reality [10]. Both { k } and { k } are to be interpreted Vortex formulation geometrically as meaningful space-time Mathematically, a vortex can be simply bivectors and not as operators. expressed by using a multi-vector Mk (k = 0, 1, 2, When we use space-time multi-vectors [5-6], for 3, 4) as follows each space-time point x on Dirac frame M M 0 M 1 M 2 M 3 M 4 { , 0,1,2,3}, there exists (9) V B iU i A B ( , A, B) x x , x x (5) where ψ=φ+iθ is a complex scalar function (wave function, but it describes mass), while The coordinates’ transformation will A=V+iU means a complex vector function be (potential function, but it describes field ) and B x x' x ; ' with (1/ 2)B as a unique bivector (spin (6) function, it can form spinor). One scalar ψ,one http://escipub.com/international-journal-of-natural-science-and-reviews/ 0003 Fred Y. Ye, IJNSR, 2017; 1:4 vector A and one bivector B just describe a | M |,A, B | (,A, B) | | M | (16) vortex and construct a physical united- measure. M | ,A, B | | (,A, B) | | M | (17) Its revision (revised conjugation) is denoted as ~ The addition, subtraction, and multiplication of M ~ ~ ~ ~ ~ ~ multi-vectors produce also multi-vectors. With M M M M M M 0 1 2 3 4 (10) definitions V B iU i ( , A,B) ~ ~ M | | M M | | M M | | M 0 and And its space-time conjugation is ~ ~ | M M || M M || M M | 0 , the M iMi M M M M M 0 1 2 3 4 (11) A B ( ,A, B) addition and multiplication will lead to various composite and superposition states, such as Physically, a linked-measure means that ψ, A, and B can be meantime measured, which just M | | M 2 | 2A| 2B| (18) constructs the mass-energy structure, including ~ ~ mass, momentum and angular momentum M | | M 2 | 2A| 2B| (19) (spin), of a vortex. At micro-particle level, a vortex M and its space-time conjugation M M | | M 2 | - 2A| 2B| (20) describe particle and anti-particle, while the M ~ | M M | 2 | 2A| 2B| (21) and its revised conjugation M reveal ~ ~ entanglement. At macro-cosmos level, M | M M | 2 | 2A| 2B| (22) means total mass-energy, and the energy-mass conservation is extended to | M M | 2 | 2A| 2B| (23) energy-mass-momentum-angular momentum joint conservation. For forming complete system, The inner product M | M produces scalar, ~ we define M M and M M . outer product | M M |and Taking an orthonormal pair of basis |↑> and <↓| | M | M | M| M leads to tensor, such as representing right-handed spin and left-handed spin or the “up” and “down” directions 2 2 2 respectively, with using Dirac bra-ket notation, M | M ( , A, B) A A B (24) we define basic states B | M | , A, B | (, A, B) | | M | (12) ~ 2 2 M | M ( , A, B) A AA B (25) M | , A, B | | (, A, B) | | M | (13) B ~ ~ | M | , A,B | ( , A,B) | | M | (14) A (B) ~ | M M | A( , A,B) A AA A(B) ~ ~ M | , A,B | | ( , A,B) | | M | (15) B B BA B(B) http://escipub.com/international-journal-of-natural-science-and-reviews/ 0004 Fred Y.
Load more

Recommended publications
  • Φ0-Magnetic Force Microscopy for Imaging and Control of Vortex
    Imaging and controlling vortex dynamics in mesoscopic superconductor-normal-metal-superconductor arrays Tyler R. Naibert1, Hryhoriy Polshyn1,2,*, Rita Garrido-Menacho1, Malcolm Durkin1, Brian Wolin1, Victor Chua1, Ian Mondragon-Shem1, Taylor Hughes1, Nadya Mason1,*, and Raffi Budakian1,3 1Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801-3080, USA 2Department of Physics, University of California, Santa Barbara, CA 93106, USA 3Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L3G1 Department of Physics, University of Waterloo, Waterloo, ON, Canada, N2L3G1 Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L2Y5 Canadian Institute for Advanced Research, Toronto, ON, Canada, M5G1Z8 *Corresponding authors. Email: [email protected]; [email protected] Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, we obtain a variety of striking spatial patterns that encode information about the energy landscape for vortices in the system. We interpret these patterns in terms of local vortex dynamics and extract the relative strengths of the characteristic energy scales in the system, such as the vortex-magnetic field and vortex-vortex interaction strengths, as well as the vortex chemical potential.
    [Show full text]
  • Scanning Hall Probe Microscopy of Vortex Matter in Single-And Two-Gap Superconductors
    ARENBERG DOCTORAL SCHOOL Faculty of Science Scanning Hall probe microscopy of vortex matter in single-and two-gap superconductors - Bart Raes Promotors: Dissertation presented in partial Prof.Dr. Victor V. Moshchalkov fulfillment of the requirements for the Prof.Dr. Jacques Tempère PhD degree July 2013 Scanning Hall probe microscopy of vortex matter in single-and two-gap superconductors Bart RAES Dissertation presented in partial fulfillment of the requirements for the PhD degree Members of the Examination committee: Prof. Dr. Victor V. Moshchalkov KU Leuven (Promotor) Prof. Dr. Jacques Tempère Universiteit Antwerpen (Co-promotor) Prof. Dr. J. Van de Vondel KU Leuven (Secretary) Prof. Dr. L. Chibotaru KU Leuven (President) Prof. Dr. J. Vanacken KU Leuven Dr. J. Gutierrez Royo KU Leuven Prof. Dr. A.V. Silhanek Université de Liège Prof. Dr. S. Bending University of Bath Prof. Dr. G. Borghs KU Leuven, IMEC July 2013 © 2013 KU Leuven, Groep Wetenschap & Technologie, Arenberg Doctoraatsschool, W. de Croylaan 6, 3001 Leuven, België Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm, elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without written permission from the publisher. ISBN 978-90-8649-638-9 D/2013/10.705/53 Dankwoord-Acknowledgements Doctoreren is niet alleen het resultaat van bijna vier jaar wetenschappelijk onderzoek, het is een lange weg met veel hindernissen maar zeker ook enkele hoogtepunten.
    [Show full text]
  • LESSONS from TOPOLOGICAL SUPERFLUIDS: SAFE and DANGEROUS ROUTES to ANTISPACETIME 1 1 1,2 Llv.B
    FEATURES LESSONS FROM TOPOLOGICAL SUPERFLUIDS: SAFE AND DANGEROUS ROUTES TO ANTISPACETIME 1 1 1,2 l V.B. Eltsov , J. Nissinen and G.E. Volovik – DOI: https://doi.org/10.1051/epn/2019504 l 1 Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland l 2 Landau Institute for Theoretical Physics, acad. Semyonov av., 1a, 142432, Chernogolovka, Russia All realistic second order phase transitions are undergone at finite transition rate and are therefore non-adiabatic. In symmetry-breaking phase transitions the non-adiabatic processes, as predicted by Kibble and Zurek [1, 2], lead to the formation of topological defects (the so-called Kibble-Zurek mechanism). The exact nature of the resulting defects depends on the detailed symmetry-breaking pattern. or example, our universe – the largest condensed topological and nontopological objects (skyrmions and matter system known to us – has undergone Q-balls), etc. several symmetry-breaking phase transitions The model predictions can be tested in particle accel- Fafter the Big Bang. As a consequence, a variety erators (now probing energy densities >10-12s after the of topological defects might have formed during the early Big Bang) and in cosmological observations (which have evolution of the Universe. Depending on the Grand Uni- not yet identified such defects to date). The same physics, fied Theory model, a number of diffierent cosmic -topo however, can be probed in symmetry breaking transitions logical defects have been predicted to exist. Among them in condensed matter systems — in fermionic superfluid are point defects, such as the 't Hooft-Polyakov magnetic 3He to an astonishing degree of similarity.
    [Show full text]
  • Twist Effects on Quantum Vortex Defects
    Journal of Physics: Conference Series PAPER • OPEN ACCESS Twist effects on quantum vortex defects To cite this article: M Foresti 2021 J. Phys.: Conf. Ser. 1730 012016 View the article online for updates and enhancements. This content was downloaded from IP address 170.106.40.40 on 26/09/2021 at 14:31 IC-MSQUARE 2020 IOP Publishing Journal of Physics: Conference Series 1730 (2021) 012016 doi:10.1088/1742-6596/1730/1/012016 Twist effects on quantum vortex defects M Foresti Department of Mathematics & Applications, University of Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy E-mail: [email protected] Abstract. We demonstrate that on a quantum vortex in Bose-Einstein condensates can form a new, central phase singularity. We define the twist phase for isophase surfaces and show that if the injection of a twist phase is global this phenomenon is given by an analog of the Aharonov- Bohm effect. We show analytically that the injection of a twist phase makes the filament unstable, that is the GP equation is modified by a new term that makes the Hamiltonian non-Hermitian. Using Kleinert's theory for multi-valued fields we show that this instability is compensated by the creation of the second vortex, possibly linked with the first one. 1. Introduction A Bose-Einstein condensate (BEC) is a diluted gas of bosons at very low temperature (see [1] and [2]) described by a unique scalar, complex-valued field = (x; t) called order parameter, that depends on position x and time t. The equation that describes the dynamics of a BEC is the Gross-Pitaevskii equation (GPE) written here in a non-dimensional [3]: i i @ = r2 + 1 − j j2 : (1) t 2 2 This is a type of non-linear Scrh¨odingerequation in three-dimensional space.
    [Show full text]
  • Generation and Detection of Continuous Variable Quantum Vortex States Via Compact Photonic Devices
    hv photonics Article Generation and Detection of Continuous Variable Quantum Vortex States via Compact Photonic Devices David Barral *, Daniel Balado and Jesús Liñares Optics Area, Department of Applied Physics, Faculty of Physics and Faculty of Optics and Optometry, University of Santiago de Compostela, Campus Vida s/n (Campus Universitario Sur), Santiago de Compostela, Galicia E-15782, Spain; [email protected] (D.B.); [email protected] (J.L.) * Correspondence: [email protected]; Tel.: +34-881-811-000 Received: 10 October 2016; Accepted: 29 December 2016; Published: 3 January 2017 Abstract: A quantum photonic circuit with the ability to produce continuous variable quantum vortex states is proposed. This device produces two single-mode squeezed states which go through a Mach-Zehnder interferometer where photons are subtracted by means of weakly coupled directional couplers towards ancillary waveguides. The detection of a number of photons in these modes heralds the production of a quantum vortex. Likewise, a measurement system of the order and handedness of quantum vortices is introduced and the performance of both devices is analyzed in a realistic scenario by means of the Wigner function. These devices open the possibility of using the quantum vortices as carriers of quantum information. Keywords: quantum information processing; continuous variables; integrated optics 1. Introduction In recent years, there has been an increasing interest in the processing of quantum information (QIP) with continuous variables (CV-QIP) [1]. CV-QIP protocols are based on Gaussian states as resources of entanglement. However, the use of non-Gaussian states has been shown to be essential in certain quantum protocols, like the entanglement distillation [2–5].
    [Show full text]
  • Physics of Superfluid Helium-4 Vortex Tangles in Normal-Fluid Strain Fields
    Physics of superfluid helium-4 vortex tangles in normal-fluid strain fields Demosthenes Kivotides1, Anthony Leonard2 1Strathclyde University, Glasgow, UK 2California Institute of Technology, Pasadena, CA, USA (Dated: March 5, 2021) Abstract By employing dimensional analysis, we scale the equations of the mesoscopic model of finite temperature superfluid hydrodynamics. Based on this scaling, we set up three problems, that depict the effects of kinematic, normal-fluid strain fields on superfluid vortex loops, and characterize small- scale processes in fully developed turbulence. We also develop a formula for the computation of energy spectra corresponding to superfluid vortex tangles in unbounded domains. Employing this formula, we compute energy spectra of superfluid vortex patterns induced by uniaxial, equibiaxial and simple-shear normal-fluid flows. By comparing the steady-state superfluid spectra and vortex structures, we conclude that normal-flow strain fields do not play important role in explaining the phenomenology of fully developed superfluid turbulence. This is in sharp contrast with the role of vortical normal-flow fields in offering plausible, structural explanations of superfluid vortex patterns and spectra entailed in numerical turbulent solutions of the mesoscopic model. 1 INTRODUCTION The advent of quantum theory posed the problem of quantizing fluid dynamics. The most obvious choice, i.e., quantizing the Navier-Stokes fluid, leads to unsurpassable mathematical difficulties with uncontrollable singularities [1]. This could be because Navier-Stokes is a statistical, dissipative field theory and, traditionally, quantum mechanics was successful operating on conservative classical field theories. Indeed, things become better with the quantization of (nonlinear) Schroedinger (NLS) type fluids, that can explain superfluidity via spontaneous breaking of the particle number symmetry which induces a ground state (superfluid) whose topological defects (superfluid vortices) interact with the fluctuations of the quantum field (normal fluid) [2–7].
    [Show full text]
  • Modeling Quantum Fluid Dynamics at Nonzero Temperatures
    Modeling quantum fluid dynamics at SPECIAL FEATURE nonzero temperatures Natalia G. Berloffa,b,1, Marc Brachetc, and Nick P. Proukakisd aDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom; bCambridge-Skoltech Quantum Fluids Laboratory, Skolkovo Institute of Science and Technology ul. Novaya, Skolkovo 143025, Russian Federation; cCentre National de la Recherche Scientifique, Laboratoire de Physique Statistique, Université Pierre-et-Marie-Curie Paris 06, Université Paris Diderot, Ecole Normale Supérieure, 75231 Paris Cedex 05, France; and dJoint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom Edited by Katepalli R. Sreenivasan, New York University, New York, NY, and approved December 13, 2013 (received for review July 15, 2013) The detailed understanding of the intricate dynamics of quantum similar [e.g., Kolmogorov spectrum (9–13)], features sensitive to fluids, in particular in the rapidly growing subfield of quantum the vortex core structure arising at lengthscales smaller than the turbulence which elucidates the evolution of a vortex tangle in average intervortex spacing [e.g., velocity statistics (20–22) and a superfluid, requires an in-depth understanding of the role of finite pressure (23)] show starkly different behavior––see, e.g., the temperature in such systems. The Landau two-fluid model is the most recent reviews (24, 25). In addition to liquid helium (2, 26), there successful hydrodynamical theory of superfluid helium, but by the has been some recent interest in the observation of turbulence in nature of the scale separations it cannot give an adequate descrip- smaller inhomogeneous confined weakly interacting gases (27, tion of the processes involving vortex dynamics and interactions.
    [Show full text]
  • A New Self-Consistent Approach of Quantum Turbulence in Superfluid
    A new self-consistent approach of quantum turbulence in superfluid helium Luca Galantucci, Andrew W. Baggaley, Carlo F. Barenghi Joint Quantum Centre Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK and Giorgio Krstulovic Universit´eC^oted'Azur, Observatoire de la C^oted'Azur, CNRS, Laboratoire Lagrange, Nice, France We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that de- scribes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is governed by a modified Navier-Stokes equa- tion. The superfluid vortex lines and normal fluid components are fully coupled in a self-consistent manner by the friction force, which induce local disturbances in the normal fluid in the vicinity of vortex lines. The main focus of this work is the numerical scheme for distributing the friction force to the mesh points where the normal fluid is defined and for evaluating the velocity of the normal fluid on the Lagrangian discretization points along the vortex lines. In particular, we show that if this numerical scheme is not careful enough, spurious results may occur. The new scheme which we propose to overcome these difficulties is based on physical principles. Finally, we apply the new method to the problem of the motion of a superfluid vortex ring in a stationary normal fluid and in a turbulent normal fluid. I. INTRODUCTION Quantum turbulence [1{3] is the disordered motion of quantum fluids - fluids which are governed by the laws of quantum mechanics rather than classical physics.
    [Show full text]
  • Half-Quantum Vortices in Superfluid Helium
    VIEWPOINT Half-Quantum Vortices in Superfluid Helium Researchers working with superfluid helium in a porous medium have generated vortices with half the quantum unit of fluid flow. by James A. Sauls∗ quantum vortex in a superfluid is a point-like hole around which the superfluid flows. This flow is quantized in the sense that the circulation—which is the sum of the velocity along a path around Athe vortex—takes on discrete values [1]. The quantum unit of circulation is h/m, where h is Planck’s constant and m is the mass of the superfluid particles. The first detection of quantized vortices with unit circulation were made in the 1960s with superfluid helium-4 and then later in su- perfluids of the lighter isotope helium-3 [2]. However, in the 1970s theorists predicted the existence of vortices with Figure 1: In superfluid helium-3, different types of quantum vortices can be observed. (Left) A ``normal'' vortex, or single half of a quantum unit of circulation in superfluid helium- quantum vortex, around which the circulation is equal to h/2m. 3 [3]. Since then, researchers have detected half-quantum This corresponds to a change of 2p in the quantum phase J. By vortices (HQVs) in diverse condensed-matter systems, from contrast, the phase a, related to the spin direction d~, remains fixed. Bose-Einstein condensates to spin-triplet superconductors (Right) A half quantum vortex has a circulation of h/4m. Both J thought to be electronic analogs of superfluid helium-3 [4]. and a change by p to give a total phase change of 2p.
    [Show full text]
  • Vortex Flux and Berry Phase in a Bose-Einstein Condensate Confined in a Toroidal Trap
    Vortex flux and Berry phase in a Bose-Einstein condensate confined in a toroidal trap Aranya B Bhattacherjee* INFM, Dipartimento di Fisica E.Fermi, Universita di Pisa, Via Buonarroti 2, I-56127, Pisa, Italy E-Mail: [email protected] Abstract: We study system of large number of singly quantized vortices in a BEC confined in a rotating toroidal geometry. Analogous to the Meissner effect in superconductors, we show that the external rotational field can be tuned to cancel the Magnus field, resulting in a zero vortex flux. We also show that the Berry’s phase for this system is directly related to the vortex flux. *Permanent Institute and address for correspondence: Department of Physics, Atma Ram Sanatan Dharma College, University of Delhi (South campus), Dhaula Kuan , New Delhi-110021, India. 1 Introduction Vortices in a superfluid formed due to rapid rotation tend to organize into a triangular lattice (also known as Abrikosov lattice) as a result of mutual repulsion. Such a lattice also has an associated rigidity. In the recent years, it has become possible to achieve such a vortex lattice state in a rapidly rotating Bose-Einstein condensate [1]. These new developments in experiments have opened a new direction for the theoretical study of quantum vortex matter, such as fractional quantum Hall like and melted vortex lattice states [2-7]. This new state of quantum vortex matter occurs only at very rapid rotations, where the system enters the “ mean field” quantum Hall regime, in which the condensation is only in lowest Landau level orbits. Eventually the vortex lattice melts, and the system enters a strongly correlated regime.
    [Show full text]
  • Phase Transition in a Chain of Quantum Vortices
    PHYSICAL REVIEW B VOLUME 59, NUMBER 2 1 JANUARY 1999-II Phase transition in a chain of quantum vortices C. Bruder* Institut fu¨r Theoretische Festko¨rperphysik, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany L. I. Glazman Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 and Delft University of Technology, 2600 GA Delft, The Netherlands A. I. Larkin Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 and L. D. Landau Institute for Theoretical Physics, Moscow 117940, Russia J. E. Mooij and A. van Oudenaarden Delft University of Technology, 2600 GA Delft, The Netherlands ~Received 8 September 1998! We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capaci- tance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array.
    [Show full text]
  • A Superfluid Theory of Everything? Marco Fedi
    A superfluid Theory of Everything? Marco Fedi To cite this version: Marco Fedi. A superfluid Theory of Everything?. 2016. hal-01312579v3 HAL Id: hal-01312579 https://hal.archives-ouvertes.fr/hal-01312579v3 Preprint submitted on 29 Jul 2016 (v3), last revised 3 May 2017 (v4) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0 International License A superuid Theory of Everything? July 29, 2016 Marco Fedi1 Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR), Italy Abstract If a real vacuum doesn't exist in quantum physics [1, 2, 3, 4, 5], by describing it as a superuid quantum space (SQS), quantum gravity can arise from attraction of space's quanta into massive particles, when they are considered superuid vortices, i.e. dynamic topological defects of SQS, given its non-zero viscosity. Gauss's law for gravity mathemati- cally supports this hypothesis, since it denes the gravitational eld as an incoming ux, and the plausibility of this mechanism has been also con- rmed through a set of CFD simulations. In this case, the gravitational eld would be an incoming ow of space's quanta and this leads to the formulation of a uid equivalence principle, able to show that gravity may be the origin of all relativistic eects, also in special relativity, producing a simplication in the theory of relativity.
    [Show full text]