Symmetries in Quantum Mechanics
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".
Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 78854
Special Issue Editor
Interests: quantum fields; symmetries and group theory; Casimir forces; vacuum fluctuations; foundations of quantum theory; history of science
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
This special issue on Symmetries in Quantum Mechanics highlights two of the most important concepts forming the foundation of modern physics: symmetry and quantum mechanics. Historically they were linked in the seminal work on the H atom and the enumeration of the periodic table. Symmetry arguments were used to determine the transition probabilities for radiation predicted by quantum theory. Since those early times the uses of symmetry in quantum theory have expanded enormously, but have not lost their roots. Symmetry properties can elucidate fundamental behaviours of quantum or classical systems in a way that shows elegance and beauty, as well as providing insight to solve many problems and to facilitate calculations. This is a golden age for experiment and theory to explore the synergy between symmetry and quantum mechanics.
Today researchers use traditional quantum theory, relativistic quantum theory, and quantum field theory, as well alternative theories such as non-linear quantum mechanics, SUSY, time asymmetric and PT symmetric quantum mechanics, stochastic electrodynamics, Bohmian mechanics, conformal field theory, quantum gravity and string theory.
Researchers are continuing to explore symmetries of the Dirac, Klein-Gordon and Schrodinger equations, the Coulomb and other potentials, van der Waals and Casimir forces, minimal coupling, nuclear structure models, and expanding their explorations to topological materials, cosmology, and systems that are dissipative, non-linear, stochastic, time dependent, non-equilibrium, or chaotic.
The symmetry principles used to analyse quantum systems include representations of symmetry groups, Lie groups, continuous and discrete symmetry transformations, symmetries for non traditional potentials and dissipative systems, geometrical, kinematical and dynamical symmetries, exact and approximate symmetries, uncertainty relations, spontaneously broken symmetry, conserved quantities that are generators of symmetry transformations, and commutation relations between symmetry operators.
The systems addressed by quantum mechanical approaches and symmetry principles have broadened to include the quantum to classical transition, for example between many-body localized and ergodic phases, and to include mesoscopic systems based on semiconductor structures or simulations at the physics-chemistry-biology interface, multiphoton entangled states, quantum crystals and quantum solids, with macroscopic quantum states and quantum sensing. With recent experimental progress and the appeal of quantum enhanced applications, the interest in macroscopic quantum effects has grown.
Quantum technologies represent a rapidly evolving field in which specific symmetry properties of quantum mechanical systems, such as superposition, entanglement and interference, are exploited to enhance the performance of various applications such as sensing, transmission, and processing of information. Some of the key approaches are based on the use of entanglement, quantum coherence, and squeezed states to revolutionize computing, measurements, and communications. This has stimulated research in different areas of physics, including quantum optics, quantum information, atomic and solid state physics, and nanoscale thermodynamics to engineer, to manipulate and to protect from environmental dephasing the fragile many-particle entangled states. Recent experiments have been done with ultracold atoms, trapped ions, superconducting qubits, spin systems, Rydberg atoms, quantum dots, atoms or photons in cavities, and quantum materials. Many of these technologies rely on the ability to control the states and degrees of freedom of atoms very precisely using electromagnetic fields, for example, using the quantum control of molecular rotation as means of encoding information. Other methods explored include the use of more general quantum correlations such as quantum discord, quantum contextuality, non-equilibrium states, and the use of phase transitions.
Quantum metrology is based in the use of entangled states and quantum correlations, and promises to provide enhanced measurement sensitivity, for example it promises frequency measurement with uncertainly at the 10^−18 level, sufficiently precise to allow exploration of violations of Lorentz invariance.
I cordially invite you to submit a paper for this special issue on whatever aspect of symmetry in quantum mechanics excites you the most.
Prof. Dr. G. Jordan Maclay
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
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Keywords
- Symmetry
- Lie groups
- Groups
- Lorentz group
- Kepler symmetry
- Phase space symmetry
- Discrete symmetry
- Hidden symmetry
- Generators of symmetry transformations
- Quantum correlations
- Quantum measurement
- Quantum sensing
- Quantum computation
- Quantum entanglement
- EPR
- Decoherence
- Superposition
- Dynamical symmetry
- Geometrical symmetry
- Kinematical symmetry
- Mesoscopic system
- Quantum-to-classical
- Uncertainty relations
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