Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0302040 · Physical review. B, Condensed matter

Manifestation of additional dimensions of space-time in mesoscopic systems

Alexander F. Andreev

Published Oct 20, 2003• 7 citations
arXivHTMLPDF

Abstract

We note that the existence of physical states which are coherent superpositions of states with even and odd numbers of fermions means the existence, together with $x,y,z,t,$ of additional spinor dimensions of space-time. A system with variable number of electrons is described in which such superpositions are realized. Experiments with mesoscopic condensed matter systems are suggested which generalize the experiment of Nakamura et al. and may provide direct observation of such superpositions and, thereby, justify the reality of a superspace with additional spinor dimensions introduced in quantum field theory to account for supersymmetry. The nature of additional dimensions of space-time is elucidated for nonrelativistic systems.

DOI
10.1103/physrevb.68.155419

Related papers

Quantum dots for demonstration of additional dimensions of spacetime

Alexander F. Andreev

By the example of electron mesoscopic systems, we show the impossibility of constraints of the quantum principle of superposition imposed by the superselection rule. This rule was introduced by Wick, Wightman, and Wigner in order to avoid the violation of Lorentz invariance due to the absence of physical invariance under rotations by an angle of 2π in states which are a coherent superposition of states with an even and odd number of fermions. We describe a mesoscopic system (a semiconductor double quantum dot at low temperatures) where such superpositions are realized; this is confirmed by experiments. We suggest a new experiment which explicitly demonstrates the absence of physical invariance under rotations by an angle of 2π. We note that an alternative to the superselection rule is the existence (along with x, y, z , and t ) of additional spinor (Grassmann) dimensions of spacetime introduced in quantum field theory for realization of supersymmetry. It is proved that additional dimensions are real; their physical meaning is clarified for nonrelativistic systems of fermions.

Journal of Experimental and Theoretical Physics•Oct 1, 2007•0 citations

Quantum Coherence Between States with Even and Odd Numbers of Electrons

Alexander F. Andreev

A system with variable number of electrons is described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace. Quantum coherence between states with even and odd numbers of electrons is of special fundamental interest. In 1952, Wick, Wightman, and Wigner [1] claimed that the coherent linear superpositions of states with even and odd numbers of fermions are incompatible with the Lorentz invariance and introduced the superselection rule, according to which such linear superpositions are physically impossible. In actuality (as was pointed out in [2, 3]), the superselection rule is the alternative to the existence, along with x, y, z, and t, of additional spinor coordinates, which, in fact, are introduced in quantum field theory to account for supersymmetry. In this work, it is proved theoretically that the superselection rule is, generally, not self-consistent. Namely, a simple realistic system with variable number of electrons is considered, which is governed by the Hamiltonian whose eigenvectors are all coherent superpositions of the

Physica Scripta•Jan 1, 2002•1 citation

Quantum coherence between states with even and odd numbers of electrons

Alexander F. Andreev

Systems with variable numbers of electrons are described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace.

Journal of Experimental and Theoretical Physics Letters•Nov 1, 2001•2 citations

Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase

Tarun Grover, D. N. Sheng, Ashvin Vishwanath

In contrast to ordinary symmetries, supersymmetry (SUSY) interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here, we theoretically show that SUSY emerges naturally in condensed matter systems known as topological superconductors. We argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display SUSY when probed at long distances and times. Experimental consequences include exact relations between quantities measured in disparate experiments and, in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken SUSY, indicating a deep relation between topological phases and SUSY.

arXiv:1301.7449•Science•Apr 4, 2014•306 citations

Production of mesoscopic superpositions with ultracold atoms

H. T. Ng

We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomena. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are macroscopic quantum superposition states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.

arXiv:0707.2398•Physical Review A•Mar 14, 2008•5 citations

Systems with Quantum Dimensions

Mikołaj Myszkowski, Mattia Damia Paciarini, Francesco Sannino

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a two-state system for which the number of spatial dimensions is represented by a quantum operator. By evaluating the corresponding partition function, we uncover a temperature-dependent effective dimension. Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.

quant-pharXiv:2511.14547•Nov 19, 2025•0 citations
We note that the existence of physical states which are coherent superpositions of states with even and odd numbers of fermions means the existence, together with x,y,z,t,x,y,z,t,x,y,z,t, of additional spinor dimensions of space-time. A system with variable number of electrons is described in which such superpositions are realized. Experiments with mesoscopic condensed matter systems are suggested which generalize the experiment of Nakamura et al. and may provide direct observation of such superpositions and, thereby, justify the reality of a superspace with additional spinor dimensions introduced in quantum field theory to account for supersymmetry. The nature of additional dimensions of space-time is elucidated for nonrelativistic systems.
By the example of electron mesoscopic systems, we show the impossibility of constraints of the quantum principle of superposition imposed by the superselection rule. This rule was introduced by Wick, Wightman, and Wigner in order to avoid the violation of Lorentz invariance due to the absence of physical invariance under rotations by an angle of 2π in states which are a coherent superposition of states with an even and odd number of fermions. We describe a mesoscopic system (a semiconductor double quantum dot at low temperatures) where such superpositions are realized; this is confirmed by experiments. We suggest a new experiment which explicitly demonstrates the absence of physical invariance under rotations by an angle of 2π. We note that an alternative to the superselection rule is the existence (along with x, y, z , and t ) of additional spinor (Grassmann) dimensions of spacetime introduced in quantum field theory for realization of supersymmetry. It is proved that additional dimensions are real; their physical meaning is clarified for nonrelativistic systems of fermions.
A system with variable number of electrons is described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace. Quantum coherence between states with even and odd numbers of electrons is of special fundamental interest. In 1952, Wick, Wightman, and Wigner [1] claimed that the coherent linear superpositions of states with even and odd numbers of fermions are incompatible with the Lorentz invariance and introduced the superselection rule, according to which such linear superpositions are physically impossible. In actuality (as was pointed out in [2, 3]), the superselection rule is the alternative to the existence, along with x, y, z, and t, of additional spinor coordinates, which, in fact, are introduced in quantum field theory to account for supersymmetry. In this work, it is proved theoretically that the superselection rule is, generally, not self-consistent. Namely, a simple realistic system with variable number of electrons is considered, which is governed by the Hamiltonian whose eigenvectors are all coherent superpositions of the
In contrast to ordinary symmetries, supersymmetry (SUSY) interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here, we theoretically show that SUSY emerges naturally in condensed matter systems known as topological superconductors. We argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display SUSY when probed at long distances and times. Experimental consequences include exact relations between quantities measured in disparate experiments and, in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken SUSY, indicating a deep relation between topological phases and SUSY.
We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomena. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are macroscopic quantum superposition states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a two-state system for which the number of spatial dimensions is represented by a quantum operator. By evaluating the corresponding partition function, we uncover a temperature-dependent effective dimension. Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.