The equivalence between the qdeformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical. Batsevych department of theoretical physics, lviv university, 290005, lviv, ukraine abstract deformationoftheheisenbergweylalgebraws ofcreationannihilationoperatorsis. It is shown that broken phase symmetry states, described by deformed coherent states, suffer phase diffusion at a rate determined by the deformation parameter. Orthogonal polynomials and deformed oscillators mafiadoc. The operator formalism has proven to be extremely useful in formulating the dual amplitudes which have ultimately lead to the string theory. This qcalculus 4 has its origin in the qdeformed harmonic oscillator theory, which, in turn, is based on the construction of a su q 2 algebra of qdeformed commutation or anticommutation. Damaskinsky, on the q oscillator and the quantum algebra suq1,1, journal of physics.
In this way, rather than a mathematical curiosity, q oscillators appear as the very basic building blocks of completely integrable dynamical systems. Studies in quantum oscillators and qdeformed quantum mechanics. Unified description of qdeformed harmonic oscillators pdf. Regarding photon and phonon as the particles obeying the multimode q deformed bosonic newton algebra, we discuss the blackbody radiation and debye model. Department of physics, dumkal college, basantapur, dumkal. The wigner operator for the qdeformed harmonic oscillator is shown to be. In this paper, we consider the dmode qdeformed bosonic newton oscillators. This qcalculus 4 has its origin in the qdeformed harmonic oscillator theory, which, in turn, is based on the construction of a su q2 algebra of qdeformed commutation or anticommutation. We therefore conclude that the usual coupled qdeformed oscillators are not suitable for the description of vibrational spectra of polyatomic molecules. Some comments on qdeformed oscillators and qdeformed su2 algebras article pdf available in european physical journal c 51 august 1997 with 27 reads how we measure reads. Modified multidimensional qdeformed newton oscillators. Since for generic q, the structure is neither commutative nor co commutative, the algebra is a nontrivial quantum algebra.
Discretization of the phase space for a qdeformed harmonic. Use keywords to narrow the search results and click on the headers to sort the results. In this way, rather than a mathematical curiosity, qoscillators appear as the very basic building blocks of completely integrable dynamical systems. Dynamics of observables in a qdeformed harmonic oscillator. In other words, oscillator can be defined as the periodic fluctuations between two things based on changes in energy. We show that an infinite set of qdeformed relevant operators close a partial qdeformed lie algebra under commutation with the arikcoon oscillator. Sogami 0 1 kouzou koizumi 0 1 0 department of physics, kyoto sangyo university, kyoto 6038555, japan 1 unified description of q deformed harmonic oscillators it is shown that a wide class of q deformed harmonic oscillators, including those of the macfarlane type and dubna type, can be described in a unified way. Ela t q ela q ela qwp ela t qwp specifications q single. The qdeformed oscillators have applications spanning diverse fields in physics.
Recently, qdeformation had been applied in cosmology to study. Moreover, at n 0 we have e n 1 2 regardless of the values of q and p. Spectral inverse problem for qdeformed harmonic oscillator. Regarding photon and phonon as the particles obeying the multimode qdeformed bosonic newton algebra, we discuss the blackbody radiation and debye model. Fibonacci oscillators1 offer a natural unification of quantum oscillators which are related to quantum groups. We study the representation of q oscillators in terms of noncommutative coordinates and show that the mirror curve of conifold appears from the commutation relation of the q oscillators. Mavrommatis, eds, university of athens, athens 1992 p. The fact that pauli principle prevails in the limit q. Pdf some comments on qdeformed oscillators and qdeformed. Thus in the classical limit the qdeformed generalized fermion theory has the same spectrum as the ordinary fermion oscillators with pauli exclusion principle. Operator formulation of qdeformed dual string model. Coates 200720 sweep oscillators a sweep waveform is another name for a sawtooth wave.
States of qdeformed oscillators coherent states and. Qdeformed oscillators as mentioned in the introduction. Just as for the ordinary quantum harmonic oscillators, we expect the zeropoint energy to play a crucial role in the correct high temperature behavior. The process of obtaining knot invariants from the q deformed algebras sun q is described in chapter 7. Kokkotas, wkb equivalent potentials for the qdeformed harmonic and anharmonic oscillators, in 2nd hellenic symposium on nuclear physics, g. Vasilievs equations, deformed oscillators and topological. Deformed su 1,1 algebra as a model for quantum oscillators. The supersymmetric quantization condition is used to study the wave functions of swkb equivalent qdeformed harmonic oscillator which are obtained by using only the knowledge of boundstate. We examine the problem of phase diffusion rate in a u1 global phase symmetry broken system, from the perspective of q deformed oscillators where the deformation parameter represents the anharmonicity. These annihilation operators satisfy the deformed commutation relations where q is a complex number. Positive feedback amplifiers oscillators lc and crystal.
The deformed oscillator systems have attracted much attention and have been considered in many. Kachurik yz ybogolyubov institute for theoretical physics, 14b metrolohichna str. We accordingly reformulate the theory of the statistical distribution function for the q deformed boson oscillators and develop an approximate theory incorporating the zeropoint energy. The process of obtaining knot invariants from the qdeformed algebras sunq is described in chapter 7. The basic numbers appropriate for this system are determined as a direct consequence of the algebra. On the nonlinearity interpretation of q andfdeformation and. Supershells in deformed harmonic oscillators and atomic. The qdeformed harmonic oscillators38,39 inspire the search for a qdeformed quantum mechanics which produce the results of standard quantum mechanics when the deformation parameter approaches a particular value. Such generalized algebras and others are further uni ed under the general rubric of deformed quantum oscillators17. This is called the algebra of the qoscillator or theqdeformed heisenberg algebra.
Various physical systems, such as excitons 23, magnons 24, trapped ions 25, or colliding atoms in boseeinstein condensates becs 26, 27 can be considered to be represented by qdeformed oscillators. In a previous paper 10, we studied a q deformed 5dimensional spacetime such that the extra dimension generates a harmonic oscillator type of potential for particles embedded in that spacetime. This is called the algebra of the q oscillator or theq deformed heisenberg algebra. The construction of qdeformed algebras, purely in terms ofqoscillators, may be extended to general u q. We examine the problem of phase diffusion rate in a u1 global phase symmetry broken system, from the perspective of qdeformed oscillators where the deformation parameter represents the anharmonicity. This wave shape is useful for changing sweeping the. Because of high frequencies, small inductance can be used for the radio frequency of oscillation. A comparative study on qdeformed fermion oscillators. The hamiltonian of the oscillator is assumed to be given by a qdeformed anticommutator of the qdeformed ladder operators. Another generalization of fermions from a different qdeformed algebra is investigated which deals with qfermions not obeying the exclusion principle. Quantum oscillator energy spectra for the generalized.
Symmetry free fulltext phase diffusion of a qdeformed. States of qdeformed oscillators coherent states and squeezed. We study the representation of qoscillators in terms of noncommutative coordinates and show that the mirror curve of conifold appears from the commutation relation of. The various relations between q deformed oscillators algebras and the q deformed su2 algebras are discussed. Studies in quantum oscillators and qdeformed quantum. Pdf first, second quantization and qdeformed harmonic oscillator. Pdf nonstandard deformed oscillators from q and p,q.
However, a di erent version of deformed oscillator, the qoscillator 30. Blackbody radiation and debye model based on qdeformed. It can be proved that the generalized deformed algebras possess a fock space of eigenvectors 0, 1. Coherent states and squeezed states of qdeformed oscillators 2. By means of the rmatrix for the quantum group glqn it is easy to show that relations 8 are. We study the dynamics of the arikcoon and anharmonic oscillators and analyze the role of q and the other. In a previous paper 10, we studied a qdeformed 5dimensional spacetime such that the extra dimension generates a harmonic oscillator type of potential for particles embedded in that spacetime. Coherent states and squeezed states of q deformed oscillators 2. Unified description of qdeformed harmonic oscillators. Then the wavefunctions for deformed oscillators are obtained for.
Search our full catalog of xo, tcxo, vcxo, ocxo, saw, mcxo, high temperature, high shock and qpl clock oscillators using the search bar andor sorting functions below. This q calculus 4 has its origin in the q deformed harmonic oscillator theory, which, in turn, is based on the construction of a su q 2 algebra of q deformed commutation or anticommutation. Q deformed oscillators as mentioned in the introduction. The dynamics is described by the multicommutator h.
These states which have arbitrary energy and momentum are. On the nonlinearity interpretation of q andfdeformation. It has been proved, however, that qdeformed fermions are fully equivalent to the ordinary fermions 43, 44, 45. For the twoparameter p, q deformed heisenberg algebra dha introduced recently and in which, instead of usual commutator of x and p in the l. Fibonacci oscillators andp,q deformed lorentz transformations. Therefore, the qdeformed oscillator algebra with the above hopf structure is really a hopf algebra. Crystal oscillators and applications a mechanical or electronic device that works on the principles of oscillation is an oscillator. These qoscillators may lead to a new kind of field theory where a small violation of the pauli exclusion principle and deviations. Department of physics, eskisehir osmangazi university. The braid group is defined and the process of obtaining knot polynomials from matrix representations of braid groups is outlined.
Here we want to make the physics point that these q deformed oscillators may have utility for the issue of ultraviolet completions since they allow for bounded. Sogami 0 1 kouzou koizumi 0 1 0 department of physics, kyoto sangyo university, kyoto 6038555, japan 1 unified description of qdeformed harmonic oscillators it is shown that a wide class of qdeformed harmonic oscillators, including those of the macfarlane type and. Just as the positive discrete series representations of su1. Unified description of q deformed harmonic oscillators. Vasilievs equations, deformed oscillators and topological open strings per sundell unab, santiago workshop on higherspin and highercurvature gravity ictpsaifr, sao paulo nov 6, 20 talk based on collaboration with boulanger and valenzuela 12 boulanger, colombo and sezgin 1012 engquist and tamassia 0507 vasiliev. Studies in quantum oscillators and qdeformed quantum mechanics thesis submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by vinod g. Studies in quantum oscillators and q deformed quantum mechanics thesis submitted in partial fulfilment of the requirements for the degree of doctor of philosophy by vinod g. These q oscillators may lead to a new kind of field theory where a small violation of the pauli exclusion principle and deviations. Tunedinput and tunedoutput oscillator tunedoutput tunedinput feedback coupling ci rf. Coupled qoscillators as a model for vibrations of polyatomic. Symmetry in nonlinear mathematical physics 1997, v. This construction leads effectively to describe interpolating statistics, which can be used to approach the properties of quasiparticle excitations occurring in manybody interacting quantum systems. The construction of q deformed algebras, purely in terms ofq oscillators, may be extended to general u q. Pdf unified description of qdeformed harmonic oscillators.
We accordingly reformulate the theory of the statistical distribution function for the qdeformed boson oscillators and develop an approximate theory incorporating the zeropoint energy. Here we want to make the physics point that these qdeformed oscillators may have utility for the issue of ultraviolet completions since they allow for bounded. Batsevych department of theoretical physics, lviv university, 290005, lviv, ukraine. The practical applications of oscillators include computers, clocks, watches, radios etc. In this work, we present a new algebraic modelby constructing the modified multidimensional qdeformed bosonic and fermionic newton oscillator algebras. Thermal radiation laws of a qdeformed boson system in m dimensions. Therefore, the q deformed oscillator algebra with the above hopf structure is really a hopf algebra. In this paper, we consider the dmode q deformed bosonic newton oscillators. Tuned oscillators radio frequency oscillators 17 tuned oscillator is a circuit that generates a radio frequency output by using lc tuned resonant circuit. Methods and applications sigma 12 2016, 047, 12 pages nonstandard deformed oscillators from q and p. With reference to a specific lrc circuit, the q factor measures the strength of a resonance. The statistical properties of the deformed dirac oscillator in one. Similar deformed oscillator algebras have been studied earlier ll1 with a view to exploring new quantization procedures. Pdf relations between the first, the second quantized representations and deform algebra are investigated.1383 632 1305 358 83 1469 438 1117 1256 728 907 872 538 246 629 1307 319 1373 50 923 925 1242 192 1441 718 617 81 259 1136 347 1326 302 333 1102 1258