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Topic Review Peer Reviewed
Undecidability and Quantum Mechanics
Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap. Since there exists no algorithm to determine whether an arbitrary quantum model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics, it infers that the existence of quantum phase transitions is an undecidable problem. 
  • 2.1K
  • 18 Oct 2022
Topic Review Peer Reviewed
Wavefunction Collapse Broadens Molecular Spectrum
Spectral lines in the optical spectra of atoms, molecules, and other quantum systems are characterized by a range of frequencies ω or a range of wavelengths λ=2πc/ω, where c is the speed of light. Such a frequency or wavelength range is called the width of the spectral lines (linewidth). It is influenced by many specific factors. Thermal motion of the molecules results in broadening of the lines as a result of the Doppler effect (thermal broadening) and by their collisions (pressure broadening). The electric fields of neighboring molecules lead to Stark broadening. The linewidth to be considered here is the so-called parametric broadening (PB) of spectral lines in the optical spectrum. PB can be considered the fundamental type of broadening of the electronic vibrational–rotational (rovibronic) transitions in a molecule, which is the direct manifestation of the basic concept of the collapse of a wavefunction that is postulated by the Copenhagen interpretation of quantum mechanics. Thus, that concept appears to be not only valid but is also useful for predicting physically observable phenomena.
  • 1.9K
  • 11 Apr 2023
Topic Review
Complementarity
In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously. An example of such a pair is position and momentum. Bohr considered one of the foundational truths of quantum mechanics to be the fact that setting up an experiment to measure one quantity of a pair, for instance the position of an electron, excludes the possibility of measuring the other, yet understanding both experiments is necessary to characterize the object under study. In Bohr's view, the behavior of atomic and subatomic objects cannot be separated from the measuring instruments that create the context in which the measured objects behave. Consequently, there is no "single picture" that unifies the results obtained in these different experimental contexts, and only the "totality of the phenomena" together can provide a completely informative description.
  • 1.9K
  • 14 Nov 2022
Topic Review
The Concept of “Quantum-Like”
The birth and spread of the prefix “quantum-” to disciplines other than physics, and the introduction of the term “quantum-like”, reflect the increasing dissatisfaction with the perceived limits and pitfalls of classic Western thought. Of course, the latter remains valuable; what is wrong is its dogmatic use and the claim of its exclusive capacity to comprehend the world. The development of quantum physics has been paralleled by the introduction of paraconsistent logics, such as fuzzy logic and dialetheism, a clear sign of the need for smoothing the inflexibility of Aristotelian logic. There is also a fil rouge (viz. an epistemological symmetry) linking the paradigm of quantum physics to ancient pre-Socratic and Eastern philosophies, suggesting the need for reappraising them in the process of reexamination of the classical thought. The increasing use of the term “quantum-like” calls for the defining and sharing of its meaning in order to properly adopt it and avoid possible misuse. 
  • 1.8K
  • 14 Mar 2022
Topic Review
Bragg Grating External Cavity Semiconductor Lasers
External cavity semiconductor lasers (ECSLs) usually refer to the gain chip based on the introduction of external optical components (such as waveguides, gratings, prisms, etc.) to provide optical feedback. By designing the type, position and structure of external optical components, the optical properties of SLs (such as center wavelength, linewidth, tuning range, side-mode suppression ratio (SMSR), etc.) can be changed. Bragg grating external cavity semiconductor laser (BG-ECSL) is a device with a specific optical element (Bragg grating) in the external cavity. BG-ECSLs have excellent performances, such as narrow linewidth, tunability and high SMSR. They are widely used in WDM systems, coherent optical communication, gas detection, Lidar, atomic physics and other fields. 
  • 1.8K
  • 09 Dec 2022
Topic Review
Loopholes in Bell Test Experiments
In Bell test experiments, there may be problems of experimental design or set-up that affect the validity of the experimental findings. These problems are often referred to as "loopholes". See the article on Bell's theorem for the theoretical background to these experimental efforts (see also John Stewart Bell). The purpose of the experiment is to test whether nature is best described using a local hidden variable theory or by the quantum entanglement theory of quantum mechanics. The "detection efficiency", or "fair sampling" problem is the most prevalent loophole in optical experiments. Another loophole that has more often been addressed is that of communication, i.e. locality. There is also the "disjoint measurement" loophole which entails multiple samples used to obtain correlations as compared to "joint measurement" where a single sample is used to obtain all correlations used in an inequality. To date, no test has simultaneously closed all loopholes. Ronald Hanson of the Delft University of Technology claims the first Bell experiment that closes both the detection and the communication loopholes. (This was not an optical experiment in the sense discussed below; the entangled degrees of freedom were electron spins rather than photon polarization.) Nevertheless, correlations of classical optical fields also violate Bell's inequality. In some experiments there may be additional defects that make "local realist" explanations of Bell test violations possible; these are briefly described below. Many modern experiments are directed at detecting quantum entanglement rather than ruling out local hidden variable theories, and these tasks are different since the former accepts quantum mechanics at the outset (no entanglement without quantum mechanics). This is regularly done using Bell's theorem, but in this situation the theorem is used as an entanglement witness, a dividing line between entangled quantum states and separable quantum states, and is as such not as sensitive to the problems described here. In October 2015, scientists from the Kavli Institute of Nanoscience reported that the Quantum nonlocality phenomenon is supported at the 96% confidence level based on a "loophole-free Bell test" study. These results were confirmed by two studies with statistical significance over 5 standard deviations which were published in December 2015. However, Alain Aspect writes that No experiment can be said to be totally loophole-free.
  • 1.7K
  • 10 Oct 2022
Topic Review
Lieb-Robinson Bounds
The Lieb-Robinson bound is a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum systems. It demonstrates that information cannot travel instantaneously in quantum theory, even when the relativity limits of the speed of light are ignored. The existence of such a finite speed was discovered mathematically by Elliott H. Lieb and Derek W. Robinson (de) in 1972. It turns the locality properties of physical systems into the existence of, and upper bound for this speed. The bound is now known as the Lieb-Robinson bound and the speed is known as the Lieb-Robinson velocity. This velocity is always finite but not universal, depending on the details of the system under consideration. For finite-range, e.g. nearest-neighbor, interactions, this velocity is a constant independent of the distance travelled. In long-range interacting systems, this velocity remains finite, but it can increase with the distance travelled. In the study of quantum systems such as quantum optics, quantum information theory, atomic physics, and condensed matter physics, it is important to know that there is a finite speed with which information can propagate. The theory of relativity shows that no information, or anything else for that matter, can travel faster than the speed of light. When non-relativistic mechanics is considered, however, (Newton's equations of motion or Schrödinger's equation of quantum mechanics) it had been thought that there is then no limitation to the speed of propagation of information. This is not so for certain kinds of quantum systems of atoms arranged in a lattice, often called quantum spin systems. This is important conceptually and practically, because it means that, for short periods of time, distant parts of a system act independently. One of the practical applications of Lieb-Robinson bounds is quantum computing. Current proposals to construct quantum computers built out of atomic-like units mostly rely on the existence of this finite speed of propagation to protect against too rapid dispersal of information. 
  • 1.6K
  • 20 Oct 2022
Biography
Hans-Peter Dürr
Hans-Peter Dürr (7 October 1929 – 18 May 2014) was a German physicist. He worked on nuclear and quantum physics, elementary particles and gravitation, epistemology, and philosophy, and he has advocated responsible scientific and energy policies.[1] In 1987, he was awarded the Right Livelihood Award for "his profound critique of the Strategic Defense Initiative (SDI) and his work to convert hi
  • 1.6K
  • 17 Nov 2022
Topic Review Peer Reviewed
Static Structures in Monatomic Fluids
The basic structural concepts in the study of monatomic fluids at equilibrium are presented in this entry. The scope encompasses both the classical and the quantum domains, the latter concentrating on the diffraction and the zero-spin boson regimes. The main mathematical objects for describing the fluid structures are the following n-body functions: the correlation functions in real space and their associated structure factors in Fourier space. In these studies, the theory of linear response to external weak fields, involving functional calculus, and Feynman’s path integral formalism are the key conceptual ingredients. Emphasis is placed on the physical implications when going from the classical domain (limit of high temperatures) to the abovementioned quantum regimes (low temperatures). In the classical domain, there is only one class of n-body structures, which at every n level consists of one correlation function plus one structure factor. However, the quantum effects bring about the splitting of the foregoing class into three path integral classes, namely instantaneous, total thermalized-continuous linear response, and centroids; each of them is associated with the action of a distinct external weak field and keeps the above n-level structures. Special attention is given to the structural pair level 𝑛=2, and future directions towards the complete study of the quantum triplet level 𝑛=3 are suggested.
  • 1.6K
  • 09 Sep 2025
Topic Review
Quantum Stream Cipher
Quantum cryptography includes quantum key distribution (QKD) and quantum stream cipher, but the researchers point out that the latter is expected as the core technology of next-generation communication systems. Various ideas have been proposed for QKD quantum cryptography, but most of them use a single-photon or similar signal. Then, although such technologies are applicable to special situations, these methods still have several difficulties to provide functions that surpass conventional technologies for social systems in the real environment. Thus, the quantum stream cipher has come to be expected as one promising countermeasure, which artificially creates quantum properties using special modulation techniques based on the macroscopic coherent state. In addition, it has the possibility to provide superior security performance than one-time pad cipher.
  • 1.5K
  • 25 May 2022
Topic Review
Event Symmetry
In physics, event symmetry includes invariance principles that have been used in some discrete approaches to quantum gravity where the diffeomorphism invariance of general relativity can be extended to a covariance under every permutation of spacetime events.
  • 1.5K
  • 07 Nov 2022
Topic Review
Beta Function
In theoretical physics, specifically quantum field theory, a beta function, β(g), encodes the dependence of a coupling parameter, g, on the energy scale, μ, of a given physical process described by quantum field theory. It is defined as and, because of the underlying renormalization group, it has no explicit dependence on μ, so it only depends on μ implicitly through g. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques.
  • 1.5K
  • 22 Nov 2022
Topic Review
Regularization
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and has proven to yield useful, accurate predictions.
  • 1.5K
  • 28 Oct 2022
Topic Review
Sakurai's Bell Inequality
The intention of a Bell inequality is to serve as a test of local realism or local hidden variable theories as against quantum mechanics, applying Bell's theorem, which shows them to be incompatible. Not all the Bell's inequalities that appear in the literature are in fact fit for this purpose. The one discussed here holds only for a very limited class of local hidden variable theories and has never been used in practical experiments. It is, however, discussed by John Bell in his "Bertlmann's socks" paper (Bell, 1981), where it is referred to as the "Wigner–d'Espagnat inequality" (d'Espagnat, 1979; Wigner, 1970). It is also variously attributed to Bohm (1951?) and Belinfante (1973). Note that the inequality is not really applicable either to electrons or photons, since it builds in no probabilistic properties in the measurement process. Much more realistic hidden variable theories can be devised, modelling spin (or polarisation, in optical Bell tests) as a vector and allowing for the fact that not all emitted particles will be detected.
  • 1.4K
  • 17 Oct 2022
Topic Review
Two-Dimensional Quantum Billiards
Two-dimensional quantum billiards are one of the most important paradigms for exploring the connection between quantum and classical worlds. Researchers are mainly focused on nonintegrable and irregular shapes to understand the quantum characteristics of chaotic billiards. The emergence of the scarred modes relevant to unstable periodic orbits (POs) is one intriguing finding in nonintegrable quantum billiards. On the other hand, stable POs are abundant in integrable billiards. The quantum wavefunctions associated with stable POs have been shown to play a key role in ballistic transport. 
  • 1.4K
  • 19 Oct 2023
Topic Review
Hidden-Measurements Interpretation
The hidden-measurements interpretation (HMI), also known as the hidden-measurements approach, is a realistic interpretation of quantum mechanics. The basis of the hidden-measurements interpretation (HMI) is the hypothesis that a quantum measurement involves a certain amount of unavoidable fluctuations in the way the measuring system interacts with the measured entity. As a consequence, the interaction is not a priori given in a quantum measurement, but is each time selected (that is, actualized, through a weighted symmetry breaking processes) when the experiment is executed; and since different measurement-interactions can produce different outcomes, this can explain why the output of a quantum measurement can only be predicted in probabilistic terms. (One should not think however of these hidden measurement-interactions to be something similar to, or to be describable in the same way as, the fundamental interactions (fundamental forces) of the standard model of particle physics, mediated by bosonic elementary entities).
  • 1.4K
  • 03 Nov 2022
Topic Review
Chirality
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.
  • 1.4K
  • 27 Oct 2022
Topic Review
Charge
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter Q, and so the invariance of the charge corresponds to the vanishing commutator [math]\displaystyle{ [Q,H]=0 }[/math], where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues q of the generator Q.
  • 1.2K
  • 14 Oct 2022
Topic Review
Colloidal Quantum Dots-Based Upconversion Devices
Colloidal quantum dots (CQD) have narrow emission linewidth and adjustable bandgap, so that CQD based infrared detectors can realize a widely tunable infrared spectral range. In addition, the luminescence spectrum of CQDs is extremely narrow, the color saturation and purity are high, and the optical stability is excellent, which can be obtained by solution procession. Therefore, CQDs-based LEDs (QLEDs) have excellent performances of a wide color gamut, long life, and low cost. For CQD baesd upconverters, except for the top electrode, the entire device can be prepared by solution method, which greatly simplifies the preparation of the device and make the upconverters are available for use in the fields of flexible devices.
  • 1.2K
  • 31 Mar 2022
Topic Review
Si-Compatible Nanostructured Photodetectors
Latest advances in the field of nanostructured photodetectors are considered, stating the types and materials, and highlighting the features of operation. Special attention is paid to the group-IV material photodetectors, including Ge, Si, Sn, and their solid solutions. Among the various designs, photodetectors with quantum wells, quantum dots, and quantum wires are highlighted. Such nanostructures have a number of unique properties, that made them striking to scientists’ attention and device applications. Nanostructures with quantum wells (QW) and quantum dots (QD) are very widely used to create photodetectors in the visible and infrared ranges. At the same time, for various applications, various semiconductor material systems are used that most fully satisfy the specific requirements for device structures: III–V (GaAs, AlGaAs, etc.), II–VI (CdHgTe), IV–IV (GeSi, GeSn, GeSiSn), and others.
  • 1.2K
  • 01 Feb 2023
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