arXiv:1711.01495 · Physical review. B./Physical review. B

Indistinguishability of quantum states and rotation counting

D. V. Averin, Christoph Bruder

Published Aug 16, 2018• 4 citations

Abstract

We consider a system that is effectively a quantum particle on a one-dimensional ring for which the points $\ensuremath{\phi}$ and $\ensuremath{\phi}+2\ensuremath{\pi}$ are indistinguishable. We show that interactions with another particle on a neighboring ring can modify the configuration space and make the points $\ensuremath{\phi}$ and $\ensuremath{\phi}+2\ensuremath{\pi}$ distinguishable. As a consequence, the orbital motion acquires a periodicity of $2\ensuremath{\pi}n$ with $n>1$ which leads to changes in the energy spectrum and in all observable properties. In particular, the fundamental magnetic flux period ${\mathrm{\ensuremath{\Phi}}}_{0}=h/q$ of the Aharonov-Bohm effect is reduced to ${\mathrm{\ensuremath{\Phi}}}_{0}/n$.

DOI: 10.1103/physrevb.98.085304

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arXiv:1711.01495 · Physical review. B./Physical review. B

Indistinguishability of quantum states and rotation counting

D. V. Averin, Christoph Bruder

Published Aug 16, 2018• 4 citations

arXiv HTML PDF

Abstract

We consider a system that is effectively a quantum particle on a one-dimensional ring for which the points

\ensuremath{\phi}

and

\ensuremath{\phi}+2\ensuremath{\pi}

are indistinguishable. We show that interactions with another particle on a neighboring ring can modify the configuration space and make the points

\ensuremath{\phi}

and

\ensuremath{\phi}+2\ensuremath{\pi}

distinguishable. As a consequence, the orbital motion acquires a periodicity of

2\ensuremath{\pi}n

with

n>1

which leads to changes in the energy spectrum and in all observable properties. In particular, the fundamental magnetic flux period

{\mathrm{\ensuremath{\Phi}}}_{0}=h/q

of the Aharonov-Bohm effect is reduced to

{\mathrm{\ensuremath{\Phi}}}_{0}/n

DOI: 10.1103/physrevb.98.085304

Related papers

The Aharonov–Bohm effect and fractional statistics of distinguishable particles

Stefan V. Mashkevich

In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.

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Fine structure and fractionalM/NAharonov-Bohm effect

Fedor Vasilievich Kusmartsev

We find a fine structure in the Aharonov-Bohm effect, which is characterized by the appearance of a type of periodic oscillation having a smaller fractional period. The effect is illustrated with the aid of a solution of the Bethe ansatz equations for N electrons located on a Hubbard ring in a magnetic field. Specifically, we found that at low density or strong coupling on a Hubbard ring in a magnetic field oscillations with three different periods occur. Along with the conventional Aharonov-Bohm oscillations with the period equal to 1, two additional oscillations with periods equal to 1/N and M/N coexist, where M is the number of down-spin particles and the periods are measured in units of the elementary flux quantum ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/e. The fine structure is due to electron-electron and Zeeman interactions. When M=N/2 there is a coexistence of the fractional 1/N and half-flux quantum periodic oscillations only. With increasing magnetic field, with the spin flips created due to Zeeman interaction, the half-flux quantum period transforms to the integer one. This transformation is not continuous but via the appearance of the fractional M/N oscillations. We discuss the relation of the described fine structure and the M/N effect to existing experiments on single and on arrays of rings, where integer and half-flux quantum periods are, respectively, observed.We find a fine structure in the Aharonov-Bohm effect, which is characterized by the appearance of a type of periodic oscillation having a smaller fractional period. The effect is illustrated with the aid of a solution of the Bethe ansatz equations for N electrons located on a Hubbard ring in a magnetic field. Specifically, we found that at low density or strong coupling on a Hubbard ring in a magnetic field oscillations with three different periods occur. Along with the conventional Aharonov-Bohm oscillations with the period equal to 1, two additional oscillations with periods equal to 1/N and M/N coexist, where M is the number of down-spin particles and the periods are measured in units of the elementary flux quantum ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/e. The fine structure is due to electron-electron and Zeeman interactions. When M=N/2 there is a coexistence of the fractional 1/N and half-flux quantum periodic oscillations only. With increasing magnetic field, with the spin flips created due to Zeeman interaction, the half-flux quantum period transforms to the integer one. This transformation is not continuous but via the appearance of the fractional M/N oscillations. We discuss the relation of the described fine structure and the M/N effect to existing experiments on single and on arrays of rings, where integer and half-flux quantum periods are, respectively, observed.

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Finite-width altermagnetic quantum rings: angular-channel hybridization and Aharonov--Bohm physics

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We study a finite-width two-dimensional quantum ring with a quadratic $d$ -wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes $m$ and $m\pm2$ angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for $N_e=1400$ and $1800$ establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.We study a finite-width two-dimensional quantum ring with a quadratic $d$-wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes $m$ and $m\pm2$ angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for $N_e=1400$ and $1800$ establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.

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Mesoscopic Aharonov-Bohm loops in a time-dependent potential: Quasistationary electronic states and quantum transitions

I. O. Kulik

Motivated by the interest to testable, exactly solvable models of quantum behavior in the time-dependent potentials, which may be important in studying (and in proof) basic quantum mechanical laws, as well as in considering the possibility of using the electronic components suggested to hypothetical ``quantum computers,'' we develop a method of solving the Schr\"odinger equation in a certain class of time-periodic and space-dependent one-dimensional potentials. In particular, it is shown that the quasistationary electronic state in the one-dimensional cyclic mesoscopic metallic ring in a rotating-potential field displays periodic variation of quasienergy in the function of magnetic flux threading the ring (the Aharonov-Bohm effect) and oscillation, superposed on the monotonous dependence, in the function of angular velocity of rotating potential (the effect similar to Rabi and/or Bloch oscillation). At large speed of rotation, quasienergy decreases rather than increases with the increase of angular velocity. The dependence of quasienergy on flux in space periodic potential displays standard $hc∕e$ periodicity as well as the periodicity with a larger period, $Nhc∕e$ , where $N$ is the number of sites in the loop, corresponding to one flux quantum per lattice site. This is an interference effect similar to one observed in the fractional quantum Hall effect but, unlike in the latter, not requiring the concept of ``fractional electron charge,'' $e∕N$ . The physical significance of the quasienergy states is clarified by studying the quantum transitions between the states as well as by investigating the energy flow between the ring and the external source of the potential.Motivated by the interest to testable, exactly solvable models of quantum behavior in the time-dependent potentials, which may be important in studying (and in proof) basic quantum mechanical laws, as well as in considering the possibility of using the electronic components suggested to hypothetical ``quantum computers,'' we develop a method of solving the Schr\"odinger equation in a certain class of time-periodic and space-dependent one-dimensional potentials. In particular, it is shown that the quasistationary electronic state in the one-dimensional cyclic mesoscopic metallic ring in a rotating-potential field displays periodic variation of quasienergy in the function of magnetic flux threading the ring (the Aharonov-Bohm effect) and oscillation, superposed on the monotonous dependence, in the function of angular velocity of rotating potential (the effect similar to Rabi and/or Bloch oscillation). At large speed of rotation, quasienergy decreases rather than increases with the increase of angular velocity. The dependence of quasienergy on flux in space periodic potential displays standard $hc∕e$ periodicity as well as the periodicity with a larger period, $Nhc∕e$, where $N$ is the number of sites in the loop, corresponding to one flux quantum per lattice site. This is an interference effect similar to one observed in the fractional quantum Hall effect but, unlike in the latter, not requiring the concept of ``fractional electron charge,'' $e∕N$. The physical significance of the quasienergy states is clarified by studying the quantum transitions between the states as well as by investigating the energy flow between the ring and the external source of the potential.

Physical Review BSep 18, 20074 citations

Magnetic flux and its topological effects in Aharonov-Bohm effect

Manvendra Somvanshi, D. Jaffino Stargen

The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, $Φ$ , due to a (classical) magnetic field, ${\mathbf B}$ , which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, $\mathbb{R}^2$ , of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, $\mathbb{R}^2-\{0\}$ , corresponding to the charge.The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, $Φ$, due to a (classical) magnetic field, ${\mathbf B}$, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, $\mathbb{R}^2$, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, $\mathbb{R}^2-\{0\}$, corresponding to the charge.

quant-pharXiv:2511.11120Nov 17, 20250 citations

We consider a system that is effectively a quantum particle on a one-dimensional ring for which the points

\ensuremath{\phi}

and

\ensuremath{\phi}+2\ensuremath{\pi}

are indistinguishable. We show that interactions with another particle on a neighboring ring can modify the configuration space and make the points

\ensuremath{\phi}

and

\ensuremath{\phi}+2\ensuremath{\pi}

distinguishable. As a consequence, the orbital motion acquires a periodicity of

2\ensuremath{\pi}n

with

n>1

which leads to changes in the energy spectrum and in all observable properties. In particular, the fundamental magnetic flux period

{\mathrm{\ensuremath{\Phi}}}_{0}=h/q

of the Aharonov-Bohm effect is reduced to

{\mathrm{\ensuremath{\Phi}}}_{0}/n

We study a finite-width two-dimensional quantum ring with a quadratic

d

-wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes

m

and

m\pm2

angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for

N_e=1400

and

1800

establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.

hc∕e

periodicity as well as the periodicity with a larger period,

Nhc∕e

, where

N

is the number of sites in the loop, corresponding to one flux quantum per lattice site. This is an interference effect similar to one observed in the fractional quantum Hall effect but, unlike in the latter, not requiring the concept of ``fractional electron charge,''

e∕N

. The physical significance of the quasienergy states is clarified by studying the quantum transitions between the states as well as by investigating the energy flow between the ring and the external source of the potential.

The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux,

Φ

, due to a (classical) magnetic field,

{\mathbf B}

, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space,

\mathbb{R}^2

, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space,

\mathbb{R}^2-\{0\}

, corresponding to the charge.