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Teorijski opis eksperimenta s dvije pukotine u supravodiču i veza s Bohmovom mehanikom

Josip Atelj

Published Sep 30, 2020• 0 citations
OpenAlex

Abstract

In this thesis we will describe theoretically a current in a superconductor on the basis of phenomenological Ginzburg-Landau equation. We will show that, in a suitable approximation, current streamlines have the same form as the Bohmian trajectories of the point-like current-carriers. Although Heisenberg inequalities prevents us from directly measuring these trajectories, we can use a Hall probe to measure a current in a superconductor and arrive at the measurements which are, in a way, averaged over a large number of particles. The experiment is envisioned on a planar superconductor having a barrier and two slits. In this case both wave and particle properties are clearly present, i.e. intereference which is manifested in particle trajectories. By measuring these quantities it would be seen how a macroscopic current exibits wave-particle properties and we would thus acquire an additional confirmation that the concept of Bohmian trajectories is not merely a hyphotethical one, but that they are, in some sense, measurable in a laboratory.

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Proposed measurement of simultaneous particle and wave properties of electric current in a superconductor

Hrvoje Nikolić, Josip Atelj

In a microscopic quantum system one cannot perform a simultaneous measurement of particle and wave properties. This, however, may not be true for macroscopic quantum systems. As a demonstration, we propose to measure the local macroscopic current passed through two slits in a superconductor. According to the theory based on the linearized Ginzburg–Landau equation for the macroscopic pseudo wave function, the streamlines of the measured current should have the same form as particle trajectories in the Bohmian interpretation of quantum mechanics. By an explicit computation we find that the streamlines should show a characteristic wiggling, which is a consequence of quantum interference.

arXiv:2003.14049•Modern Physics Letters A•Oct 23, 2020•1 citation

Gebonden Toestanden en Stromen

Krekels, Simon

This thesis comprises a wide range of topics. The first work revolves around an active matter system, where a bound state between two run-and-tumble probe particles is induced by a thermal medium, whose interactions with the probe are purely repulsive. The bound state is then induced by the self-trapping behavior of the active particles and the density profile of the thermal particles. There is a surprising analogy between the formation of these bound states and the formation of Cooper pairs in superconductors. The electron, as described by the Dirac equation, may be seen as obeying a master equation of precisely the same form as the master equation of the run-and-tumble particle. Taking this view literally, Cooper pairs are bound states of two run-and-tumble particles whose binding is enabled by the thermal medium in which they reside. The second chapter revolves around these zig-zag electrons which are described by this master-equation formulation of the Dirac equation. This zig-zag behavior may be visualized by the calculation of trajectories that form an extension of Bohmian trajectories. These tools of visualization are then applied to the famous Stern-Gerlach experiment. The third part of the thesis concerns superconductivity, and more specifically the Josephson effect. Josephson junctions form the cornerstone of superconducting quantum technology, providing anharmonicity to qubits and phase sensitivity to SQUIDs. The physics of Josephson junctions is very rich, with features such as Andreev bound states playing a crucial part in the understanding of the Josephson current and the current-phase relation. Yet the microscopic modeling of Josephson junctions remains challenging, and many things remain unexplained. One of the issues addressed in this thesis is the issue of current conservation in the modeling of Josephson junctions, but also in mean-field superconductivity generally. We show that ensuring current conservation has a dramatic effect on the Andreev states and on the current-phase relation, challenging assumptions which have long become standard in the literature. The final part of the thesis is concerned with superconducting qubits, and the effect of the precise shape of the CPR on qubit properties. We uncover resonances of the Andreev bound states, and show that these resonances correspond to lessened anharmonicity for transmon qubits.

•Nov 10, 2025•0 citations

Bohm’s Quantum Potential and Quantum Force in Superconductor

А. В. Никулов, Luigi Accardi, Guillaume Adenier +5 more

The Bohm’s quantum potential, introduced in 1952, and the quantum force in superconductor, introduced in 2001, allow to describe non‐local force‐free momentum transfer observed in the Ahronov‐Bohm effects. Comparison of the Ahronov‐Bohm effects in the two‐slit interference experiment and in superconductor ring reveals fundamental difference between the Schrodinger wave function and the wave function describing macroscopic quantum phenomena. The Ginzburg‐Landau wave function describing the superconductivity phenomenon can not collapse and an additional postulate, which was implied first by L.D. Landau, must be used for the description of macroscopic quantum phenomena. It is note that quantum principles and postulates should not be universal till the quantum formalism is only phenomenological theory but no description of an unique reality.

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Bohmian Mechanics: Towards Illuminating The Quantum Potential

Matthew J. Brown

This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.

•Feb 20, 2018•1 citation

Vertices and vortices in high Tc superconductors

Mohammad Hadi Sharifzadeh Amin

This thesis is organized in two independent parts, in which I study two different aspects of high Tc superconductivity. The first part begins with an introduction aimed to briefly introduce some relevant experimental and theoretical works performed in recent years, that have helped us to think about cuprates the way we do now. Afterwards, I introduce Landau Fermi liquid theory in a standard text book way. The question of validity of Fermi liquid theory in 2-d is then raised and investigated by searching for singularities in Landau's /-function. I show that the interaction function between two quasiparticles whose momenta approach each other near a curved point of the Fermi surface, contains a 1-d singularity not strong enough to change the Fermi liquid behavior. On the other hand, inflection points provide 2-d singularities that have to be taken seriously in Fermi liquid considerations. I then introduce nearly antiferromagnetic Fermi liquid theory (NAFL), which is a phenomenological theory proposed to describe high Tc systems. I mainly focus on the self-consistency of the theory in calculations. I criticize the theory on the basis of overlooking the vertex corrections in the strong coupling calculations of the transition temperature Tc. I calculate the first vertex correction for an optimally doped system and show that it is of the same order of magnitude as the bare vertex. Migdal's theorem is therefore not valid and Eliashberg formalism is not applicable to this situation. The same conclusion is obtained even after inclusion of the quasiparticle residue Z to the calculation. The sign of the vertex correction is then considered. I show that the positive sign of the vertex correction for the optimally doped system requires a phase transition of some sort as the doping is decreased. Part II of the thesis is devoted to the vortex lattice properties of high Tc superconductors. I establish a method to study vortex lattice properties of d-wave superconductors based on a generalization of the London model. The method has the advantage of simplicity as well as having very few free parameters (one at most) compared to other methods. The generalized London free energy is obtained from an s-d mixing Ginsburg-Landau free energy and also from the microscopic theory of Gorkov. The generalized London equation is found to be analytic at high temperatures. At very low temperatures however nonanalyticities arise as a result of the nodes on the superconducting gap. I then present the results of our calculations of some measurable quantities, such as the vortex lattice geometry and the effective penetration depth (as denned in μSR experiments). Comparison between our results and different experimental data is then performed. Especially our prediction for the magnetic field dependence of the effective penetration depth at T = 0, which is recently observed in //SR experiments with excellent agreement, is discussed.

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The (un)detectability of trajectories in pilot-wave theory

Johannes Fankhauser

Abstract Pilot wave theory endows particles with de nite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment. This idea might seem to be contested in light of two proposals: (1) So-called ‘weak velocity measurements’, allegedly detecting Bohmian trajectories by weakly probing a quantum system without essentially disturbing it, and (2) the so-called ‘surrealistic’ trajectories experiment which supposedly establishes a conflict between the ‘actual’ position of a particle and its position derived from pilot wave theory. Although both attempts shed light on the nature of Bohmian particles, neither constitute empirical or theoretical evidence in favour or against pilot wave theory. Both instances admit a straightforward standard quantum mechanical interpretation compatible with the predictions of Bohmian theories. It is concluded that the puzzles arise from the absence of a coherent account of what quantum mechanical measurements signify.

arXiv:2503.07694•Apr 1, 2025•0 citations
In this thesis we will describe theoretically a current in a superconductor on the basis of phenomenological Ginzburg-Landau equation. We will show that, in a suitable approximation, current streamlines have the same form as the Bohmian trajectories of the point-like current-carriers. Although Heisenberg inequalities prevents us from directly measuring these trajectories, we can use a Hall probe to measure a current in a superconductor and arrive at the measurements which are, in a way, averaged over a large number of particles. The experiment is envisioned on a planar superconductor having a barrier and two slits. In this case both wave and particle properties are clearly present, i.e. intereference which is manifested in particle trajectories. By measuring these quantities it would be seen how a macroscopic current exibits wave-particle properties and we would thus acquire an additional confirmation that the concept of Bohmian trajectories is not merely a hyphotethical one, but that they are, in some sense, measurable in a laboratory.
In a microscopic quantum system one cannot perform a simultaneous measurement of particle and wave properties. This, however, may not be true for macroscopic quantum systems. As a demonstration, we propose to measure the local macroscopic current passed through two slits in a superconductor. According to the theory based on the linearized Ginzburg–Landau equation for the macroscopic pseudo wave function, the streamlines of the measured current should have the same form as particle trajectories in the Bohmian interpretation of quantum mechanics. By an explicit computation we find that the streamlines should show a characteristic wiggling, which is a consequence of quantum interference.
This thesis comprises a wide range of topics. The first work revolves around an active matter system, where a bound state between two run-and-tumble probe particles is induced by a thermal medium, whose interactions with the probe are purely repulsive. The bound state is then induced by the self-trapping behavior of the active particles and the density profile of the thermal particles. There is a surprising analogy between the formation of these bound states and the formation of Cooper pairs in superconductors. The electron, as described by the Dirac equation, may be seen as obeying a master equation of precisely the same form as the master equation of the run-and-tumble particle. Taking this view literally, Cooper pairs are bound states of two run-and-tumble particles whose binding is enabled by the thermal medium in which they reside. The second chapter revolves around these zig-zag electrons which are described by this master-equation formulation of the Dirac equation. This zig-zag behavior may be visualized by the calculation of trajectories that form an extension of Bohmian trajectories. These tools of visualization are then applied to the famous Stern-Gerlach experiment. The third part of the thesis concerns superconductivity, and more specifically the Josephson effect. Josephson junctions form the cornerstone of superconducting quantum technology, providing anharmonicity to qubits and phase sensitivity to SQUIDs. The physics of Josephson junctions is very rich, with features such as Andreev bound states playing a crucial part in the understanding of the Josephson current and the current-phase relation. Yet the microscopic modeling of Josephson junctions remains challenging, and many things remain unexplained. One of the issues addressed in this thesis is the issue of current conservation in the modeling of Josephson junctions, but also in mean-field superconductivity generally. We show that ensuring current conservation has a dramatic effect on the Andreev states and on the current-phase relation, challenging assumptions which have long become standard in the literature. The final part of the thesis is concerned with superconducting qubits, and the effect of the precise shape of the CPR on qubit properties. We uncover resonances of the Andreev bound states, and show that these resonances correspond to lessened anharmonicity for transmon qubits.
The Bohm’s quantum potential, introduced in 1952, and the quantum force in superconductor, introduced in 2001, allow to describe non‐local force‐free momentum transfer observed in the Ahronov‐Bohm effects. Comparison of the Ahronov‐Bohm effects in the two‐slit interference experiment and in superconductor ring reveals fundamental difference between the Schrodinger wave function and the wave function describing macroscopic quantum phenomena. The Ginzburg‐Landau wave function describing the superconductivity phenomenon can not collapse and an additional postulate, which was implied first by L.D. Landau, must be used for the description of macroscopic quantum phenomena. It is note that quantum principles and postulates should not be universal till the quantum formalism is only phenomenological theory but no description of an unique reality.
This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.
This thesis is organized in two independent parts, in which I study two different aspects of high Tc superconductivity. The first part begins with an introduction aimed to briefly introduce some relevant experimental and theoretical works performed in recent years, that have helped us to think about cuprates the way we do now. Afterwards, I introduce Landau Fermi liquid theory in a standard text book way. The question of validity of Fermi liquid theory in 2-d is then raised and investigated by searching for singularities in Landau's /-function. I show that the interaction function between two quasiparticles whose momenta approach each other near a curved point of the Fermi surface, contains a 1-d singularity not strong enough to change the Fermi liquid behavior. On the other hand, inflection points provide 2-d singularities that have to be taken seriously in Fermi liquid considerations. I then introduce nearly antiferromagnetic Fermi liquid theory (NAFL), which is a phenomenological theory proposed to describe high Tc systems. I mainly focus on the self-consistency of the theory in calculations. I criticize the theory on the basis of overlooking the vertex corrections in the strong coupling calculations of the transition temperature Tc. I calculate the first vertex correction for an optimally doped system and show that it is of the same order of magnitude as the bare vertex. Migdal's theorem is therefore not valid and Eliashberg formalism is not applicable to this situation. The same conclusion is obtained even after inclusion of the quasiparticle residue Z to the calculation. The sign of the vertex correction is then considered. I show that the positive sign of the vertex correction for the optimally doped system requires a phase transition of some sort as the doping is decreased. Part II of the thesis is devoted to the vortex lattice properties of high Tc superconductors. I establish a method to study vortex lattice properties of d-wave superconductors based on a generalization of the London model. The method has the advantage of simplicity as well as having very few free parameters (one at most) compared to other methods. The generalized London free energy is obtained from an s-d mixing Ginsburg-Landau free energy and also from the microscopic theory of Gorkov. The generalized London equation is found to be analytic at high temperatures. At very low temperatures however nonanalyticities arise as a result of the nodes on the superconducting gap. I then present the results of our calculations of some measurable quantities, such as the vortex lattice geometry and the effective penetration depth (as denned in μSR experiments). Comparison between our results and different experimental data is then performed. Especially our prediction for the magnetic field dependence of the effective penetration depth at T = 0, which is recently observed in //SR experiments with excellent agreement, is discussed.
Abstract Pilot wave theory endows particles with de nite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment. This idea might seem to be contested in light of two proposals: (1) So-called ‘weak velocity measurements’, allegedly detecting Bohmian trajectories by weakly probing a quantum system without essentially disturbing it, and (2) the so-called ‘surrealistic’ trajectories experiment which supposedly establishes a conflict between the ‘actual’ position of a particle and its position derived from pilot wave theory. Although both attempts shed light on the nature of Bohmian particles, neither constitute empirical or theoretical evidence in favour or against pilot wave theory. Both instances admit a straightforward standard quantum mechanical interpretation compatible with the predictions of Bohmian theories. It is concluded that the puzzles arise from the absence of a coherent account of what quantum mechanical measurements signify.