It is noted that the elementary electric charge is equal to e , from which fact the well-known principle of quantization of the electric charge definitely follows, namely, the electric charge is quantized and a quantum is the charge of the electron e (or positron). Or any change in the charge is equal to an integer number of electrons (or positrons). The formally identical transformation of the principle of quantization of the electric charge allows formulating the principle of quantization of the magnetic flux, namely, the quantity inverse to the magnetic flux is quantized and a quantum is the inverse of the quantum of the F. London magnetic flux. Or any change in the reciprocal of the magnetic flux is equal to an integer number of quantities inverse to the quantum of the F. London magnetic flux. The reciprocal of the magnetic flux quantum is equal to the sum of two quantities inverse to the quantum of the F. London magnetic flux. The validity of the principle of quantization of the magnetic flux with respect to the hydrogen atom is illustrated by Theorem 1: quantization of the energy of the hydrogen atom is a consequence of the principle of quantization of the magnetic flux. Theorem 2 is proved: the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. Theorem 3 is proved: the quantum of the magnetic flux is not the minimum possible for a nonzero magnetic flux. It is established that the quantum of the magnetic flux is not a quantum in the sense of a portion (like the F. London quantum). A quantum is the inverse of the quantum of the F. London magnetic flux. It is established that the magnitude of the magnetic flux quantum is not the minimum possible for a nonzero magnetic flux. It is established that the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. A discrete set of energies of the hydrogen atom is noted to be a consequence of the solution of the Schrödinger equation, which, in turn, is phenomenological. The reverse discourse used in the proof of Theorem 1 can show that the Schrödinger equation is a consequence of the principle of quantization of the magnetic flux.It is noted that the elementary electric charge is equal to e , from which fact the well-known principle of quantization of the electric charge definitely follows, namely, the electric charge is quantized and a quantum is the charge of the electron e (or positron). Or any change in the charge is equal to an integer number of electrons (or positrons). The formally identical transformation of the principle of quantization of the electric charge allows formulating the principle of quantization of the magnetic flux, namely, the quantity inverse to the magnetic flux is quantized and a quantum is the inverse of the quantum of the F. London magnetic flux. Or any change in the reciprocal of the magnetic flux is equal to an integer number of quantities inverse to the quantum of the F. London magnetic flux. The reciprocal of the magnetic flux quantum is equal to the sum of two quantities inverse to the quantum of the F. London magnetic flux. The validity of the principle of quantization of the magnetic flux with respect to the hydrogen atom is illustrated by Theorem 1: quantization of the energy of the hydrogen atom is a consequence of the principle of quantization of the magnetic flux. Theorem 2 is proved: the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. Theorem 3 is proved: the quantum of the magnetic flux is not the minimum possible for a nonzero magnetic flux. It is established that the quantum of the magnetic flux is not a quantum in the sense of a portion (like the F. London quantum). A quantum is the inverse of the quantum of the F. London magnetic flux. It is established that the magnitude of the magnetic flux quantum is not the minimum possible for a nonzero magnetic flux. It is established that the magnetic flux of a hydrogen atom in the ground state is equal to the quantum of the F. London magnetic flux. A discrete set of energies of the hydrogen atom is noted to be a consequence of the solution of the Schrödinger equation, which, in turn, is phenomenological. The reverse discourse used in the proof of Theorem 1 can show that the Schrödinger equation is a consequence of the principle of quantization of the magnetic flux.

Izvestia Ufimskogo Nauchnogo Tsentra RANDec 11, 20203 citations

Real time observation of a stationary magneton

Emmanouil N. Markoulakis, Antonios J. Konstantaras, J. Chatzakis +2 more

The magnetic dipole field geometry of subatomic elementary particles like the electron differs from the classical macroscopic field imprint of a bar magnet. It resembles more like an eight figure or else joint double quantum-dots instead of the classical, spherical more uniform field of a bar magnet. This actual subatomic quantum magnetic field of an electron at rest, is called Quantum Magnet or else a Magneton. It is today verified experimentally by quantum magnetic field imaging methods and sensors like SQUID scanning magnetic microscopy of ferromagnets and also seen in Bose-Einstein Condensates (BEC) quantum ferrofluids experiments. Normally, a macroscale bar magnet should behave like a relative giant Quantum Magnet with identical magnetic dipole field imprint since all of its individual magnetons collectively inside the material, dipole moments are uniformly aligned forming the total net field of the magnet. However due to Quantum Decoherence (QDE) phenomenon at the macroscale and macroscopic magnetic field imaging sensors limitations which cannot pickup these rapid quantum magnetization fluctuations, this field is masked and not visible at the macroscale. By using the relative inexpensive submicron resolution Ferrolens quantum magnetic optical superparamagnetic thin film sensor for field real time imaging and method we have researched in our previous publications, we can actually make this net magneton field visible on macroscale magnets. We call this net total field herein, Quantum Field of Magnet (QFM) differentiating it therefore from the field of the single subatomic magneton thus quantum magnet. Additionally, the unique potential of the Ferrolens device to display also the magnetic flux lines of this macroscopically projected giant Magneton gives us the opportunity for the first time to study the individual magnetic flux lines geometrical pattern that of a single subatomic magneton. We describe this particular magnetic flux of the magneton observed, quantum magnetic flux. Therefore an astonishing novel observation has been made that the Quantum Magnetic Field of the Magnet-Magneton (QFM) consists of a dipole vortex shaped magnetic flux geometrical pattern responsible for creating the classical macroscopic N-S field of magnetism as a tension field between the two polar quantum flux vortices North and South poles. A physical interpretation of this quantum decoherence mechanism observed is analyzed and presented and conclusions made showing physical evidence of the quantum origin irrotational and therefore conservative property of magnetism and also demonstrating that ultimately magnetism at the quantum level is an energy dipole vortex phenomenon.The magnetic dipole field geometry of subatomic elementary particles like the electron differs from the classical macroscopic field imprint of a bar magnet. It resembles more like an eight figure or else joint double quantum-dots instead of the classical, spherical more uniform field of a bar magnet. This actual subatomic quantum magnetic field of an electron at rest, is called Quantum Magnet or else a Magneton. It is today verified experimentally by quantum magnetic field imaging methods and sensors like SQUID scanning magnetic microscopy of ferromagnets and also seen in Bose-Einstein Condensates (BEC) quantum ferrofluids experiments. Normally, a macroscale bar magnet should behave like a relative giant Quantum Magnet with identical magnetic dipole field imprint since all of its individual magnetons collectively inside the material, dipole moments are uniformly aligned forming the total net field of the magnet. However due to Quantum Decoherence (QDE) phenomenon at the macroscale and macroscopic magnetic field imaging sensors limitations which cannot pickup these rapid quantum magnetization fluctuations, this field is masked and not visible at the macroscale. By using the relative inexpensive submicron resolution Ferrolens quantum magnetic optical superparamagnetic thin film sensor for field real time imaging and method we have researched in our previous publications, we can actually make this net magneton field visible on macroscale magnets. We call this net total field herein, Quantum Field of Magnet (QFM) differentiating it therefore from the field of the single subatomic magneton thus quantum magnet. Additionally, the unique potential of the Ferrolens device to display also the magnetic flux lines of this macroscopically projected giant Magneton gives us the opportunity for the first time to study the individual magnetic flux lines geometrical pattern that of a single subatomic magneton. We describe this particular magnetic flux of the magneton observed, quantum magnetic flux. Therefore an astonishing novel observation has been made that the Quantum Magnetic Field of the Magnet-Magneton (QFM) consists of a dipole vortex shaped magnetic flux geometrical pattern responsible for creating the classical macroscopic N-S field of magnetism as a tension field between the two polar quantum flux vortices North and South poles. A physical interpretation of this quantum decoherence mechanism observed is analyzed and presented and conclusions made showing physical evidence of the quantum origin irrotational and therefore conservative property of magnetism and also demonstrating that ultimately magnetism at the quantum level is an energy dipole vortex phenomenon.

arXiv:1911.05735Results in PhysicsNov 8, 201924 citations

Quantum Magnetism

Ulrich Schollwöck, Johannes Richter, DAMIAN J. J. FARNELL +1 more

Lecture notes in physicsJan 1, 2004156 citations

Quantum magnetism

Schollwöck, Ulrich, DAMIAN J. J. FARNELL, Bishop, Ray +1 more

Jan 1, 20040 citations

Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems

Shunsuke C. Furuya, Masahiro Sato

The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe et al., Phys. Rev. B 103, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems. The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe et al., Phys. Rev. B 103, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems. The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.

arXiv:2108.08458Physical review. B./Physical review. BNov 1, 20215 citations

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at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.