<i>Zitterbewegung</i>by quantum field-theory considerations

Wang, Zhiyong; Xiong, Cai-Dong

doi:10.1103/physreva.77.045402

Cited by 23 publications

(22 citation statements)

References 10 publications

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“…In quantum field theory, a superposition of positiveand negative-energy wave functions is deemed physically impossible. However, a hole theory [6,37] describes that a hole can be seen as a positron, and Wang and Xiong [11] argued that therefore quantum field theory may still allow the existence of Zitterbewegung.…”

Section: Dirac Equation Vs Dirac-like Systemmentioning

confidence: 99%

“…However, this concept is controversial and was challenged by Krekora et al [10]. The existence of Zitterbewegung, in relativistic quantum mechanics and in quantum field theory, has been a recurrent subject of discussion over the past years [10][11][12]. The interest in Zitterbewegung was recently rekindled due to its analog in Dirac-like systems [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Propagation of a relativistic electron wave packet in the Dirac equation

Park

2012

Phys. Rev. A

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Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.

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Section: Dirac Equation Vs Dirac-like Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Propagation of a relativistic electron wave packet in the Dirac equation

Park

2012

Phys. Rev. A

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“…[33] using a different approach. For many systems [5,[7][8][9][10][11][12][13][14][15][16][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] the Hamiltonian can be written in a quite general form:…”

Section: Spin In An Effective Magnetic Fieldmentioning

confidence: 99%

General theory of Zitterbewegung

Dávid

Cserti

2010

Phys. Rev. B

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We derive a general and simple expression for the time-dependence of the position operator of a multi-band Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasi-particle. Our result shows that in such systems the Zitterbewegung like term related to a trembling motion of the quasi-particle, always appears in the position operator. Moreover, the Zitterbewegung is, in general, a multi-frequency oscillatory motion of the quasi-particle. We derive a few different expressions for the amplitude of the oscillatory motion including that related to the Berry connection matrix. We present several examples to demonstrate how general and versatile our result is.PACS numbers: 71.70.Ej,73.22.Pr,03.65.Vf Schrödinger in his original paper has predicted a 'trembling' or in other words a rapid oscillatory motion of the center of the free wave packet for relativistic electron [1]. However, the Zitterbewegung is not strictly a relativistic effect [2-6] but can be observed in spintronic systems as well [7]. This work has initiated many other works with an aim to demonstrate the appearance of the Zitterbewegung not only for relativistic Dirac electrons. In these works a common feature is that the oscillatory motion of the free particles can be described only by one frequency.In our previous work we showed that for a wide class of Hamiltonians related to for example spintronic systems and graphene, the Zitterbewegung can be treated in a unified way [33]. Here the basic idea was that the Hamiltonian of several systems can be mapped to that modelling the precession of a virtual spin in an effective magnetic field. The coupled equations for this virtual spin precession and the orbital motion of the quasi-particle can easily be solved. Thus, the Zitterbewegung is arising because the virtual spin and the orbital motion for the quasi-particle are coupled. Our work suggests as natural question whether the phenomenon of the Zitterbewegung also arises for an even more general Hamiltonian.In the present work we extend the Zitterbewegung phenomena to a broader class of quantum Hamiltonians for free (quasi-) particles. In particularly, we derive a general and simple expression for the time-dependence of the position operator x(t) for a multi-band Hamiltonian given bywhere each matrix element is a differentiable function of the momentum p of the particle itself and n ≥ 2 is the number of degrees of freedom of the system. From our general expression for the position operator x(t) we shall show that i) the Zitterbewegung always appears for systems given by the Hamiltonian (1), i) for n > 2 the Zitterbewegung is in fact a multi-component oscillatory motion of the free quasi-particle, ii) for n = 2 we recover the results obtained earlier in the above mentioned references. To find the time dependence of the position operator x(t) of the quasi-particle in Heisenberg picture one needs to calculatewhere x(0) is the position operator at t = 0, ie, it equals to the position operator in Schrödinger picture. Because the mom...

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“…It arises as an interference effect between the positive and negative energy parts of the spinor and does not appear for spinors that consist entirely of positive (or negative) energy. The real existence of Zitterbewegung, in relativistic quantum mechanics and in quantum field theory, has been a recurrent subject of discussion in the last years [24,25]. Lamata et al suggested [18] that the physics of a free Dirac particle could be simulated using an ion with four internal states and a set of laser beams coupling these states to the three harmonic oscillators describing the ion motion in the trapping potential.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of relativistic quantum physics with trapped ions

Roos¹,

Gerritsma²,

Kirchmair³

et al. 2011

J. Phys.: Conf. Ser.

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Abstract. Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions' internal states. This mechanism can be used for high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, spin-motion interactions are also of interest for the purpose of quantum simulations where the motional state no longer acts as an auxiliary quantum system only. Here, we describe an experiment where a laser-cooled trapped ion is set to behave as a free relativistic quantum particle. IntroductionQuantum simulation aims at simulating a quantum system of interest with a controllable laboratory system described by the same mathematical model. In this way, it might be possible to simulate quantum systems that can neither be efficiently simulated on a classical computer [1] nor easily accessed experimentally. For this, the laboratory system needs to be very well understood in terms of the Hamiltonian describing it. To turn it into a useful quantum simulator, it should allow for parameter tunability and for the measurement of observables that provide important insights into the physics of the system to be simulated. There are two types of quantum simulators currently discussed in the literature. Digital quantum simulators [2,3,4] try to translate the unitaries describing the system dynamics into quantum circuits consisting of elementary gate operations. In this approach, a universal quantum computer could be used for efficiently simulating all quantum systems with local interactions [2]. The second class, that one might call analogue quantum simulators, builds on the principle of engineering a system having exactly the Hamiltonian one is interested in. The main motivation behind these approaches is to find solutions of problems in quantum-many body physics that cannot be efficiently simulated on classical computers. Examples include quantum phase transitions, quantum magnetism or high-temperature superconductivity.Many proposals and experiments in this area currently focus on neutral atoms trapped in optical lattices as a possible quantum simulator [5]. The parallelism that is naturally occurring

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Zitterbewegungby quantum field-theory considerations

Abstract: The validity of the work by Lamata et al. ͓Phys. Rev. Lett. 98, 253005 ͑2007͔͒ can be further shown by quantum field-theory considerations.

Cited by 23 publications

References 10 publications

Propagation of a relativistic electron wave packet in the Dirac equation

Propagation of a relativistic electron wave packet in the Dirac equation

General theory of Zitterbewegung

Quantum simulation of relativistic quantum physics with trapped ions

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