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Karol Życzkowski
Karol Życzkowski (born 1960) is a Polish physicist and mathematician. He is a professor of physics at the Atomic Physics Department, Institute of Physics, of the Jagiellonian University in Kraków, Poland, and also at the Center for Theoretical Physics of the Polish Academy of Sciences in Warsaw. He worked as a Humboldt Fellow at the University of Essen (1989–1990) and as senior Fulbright Fellow at the University of Maryland, College Park (1996/97). In 2005/06 visiting scientist at the Perimeter Institute, Waterloo (Ontario). Member of Academia Europaea since 2014. Życzkowski was a member of the Commission on European Matters PAU created by the Polish Academy of Learning. Życzkowski has contributed to quantum chaos, quantum measurement, entropy, and entanglement, the theory of voting and jointly with Wojciech Słomczyński designed thJagiellonian Compromise- a voting system for the Council of the European Union. He worked on complex Hadamard matrices, numerical range In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kraków
, officially the Royal Capital City of Kraków, is the List of cities and towns in Poland, second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city has a population of 804,237 (2023), with approximately 8 million additional people living within a radius. Kraków was the official capital of Poland until 1596, and has traditionally been one of the leading centres of Polish academic, cultural, and artistic life. Cited as one of Europe's most beautiful cities, its Kraków Old Town, Old Town was declared a UNESCO World Heritage Site in 1978, one of the world's first sites granted the status. The city began as a Hamlet (place), hamlet on Wawel Hill and was a busy trading centre of Central Europe in 985. In 1038, it became the seat of King of Poland, Polish monarchs from the Piast dynasty, and subsequently served as the centre of administration under Jagiellonian dynasty, Jagiellonian kings and of the Polish–Lithuan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of Academia Europaea
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament * The Members The Members is a British punk rock, punk band that originated in Camberley, Surrey, England. In the UK, they are best known for their single "The Sound of the Suburbs", reaching No. 12 in the UK Singles Chart in 1979, and in Australia, "Radio" ..., a British punk rock band * Meronymy, a semantic relationship in linguistics * Church m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Range
In the mathematics, mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex number, complex n \times n square matrix, matrix ''A'' is the set :W(A) = \left\ = \left\ where \mathbf^* denotes the conjugate transpose of the vector (mathematics), vector \mathbf. The numerical range includes, in particular, the diagonal entries of the matrix (obtained by choosing ''x'' equal to the unit vectors along the coordinate axes) and the eigenvalues of the matrix (obtained by choosing ''x'' equal to the eigenvectors). In engineering, numerical ranges are used as a rough estimate of eigenvalues of ''A''. Recently, generalizations of the numerical range are used to study quantum computing. A related concept is the numerical radius, which is the largest absolute value of the numbers in the numerical range, i.e. :r(A) = \sup \ = \sup_ , \langle\mathbf, A\mathbf \rangle, . Properties Let sum of sets denote a sumset. General properties # The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Hadamard Matrix
A complex Hadamard matrix is any complex N \times N matrix H satisfying two conditions: *unimodularity (the modulus of each entry is unity): , H_, = 1 \text j,k = 1,2,\dots,N *orthogonality: HH^ = NI, where \dagger denotes the Hermitian transpose of H and I is the identity matrix. The concept is a generalization of Hadamard matrices. Note that any complex Hadamard matrix H can be made into a unitary matrix by multiplying it by \frac; conversely, any unitary matrix whose entries all have modulus \frac becomes a complex Hadamard upon multiplication by \sqrt. Complex Hadamard matrices arise in the study of operator algebras and the theory of quantum computation. Real Hadamard matrices and Butson-type Hadamard matrices form particular cases of complex Hadamard matrices. Complex Hadamard matrices exist for any natural number N (compare with the real case, in which Hadamard matrices do not exist for every N and existence is not known for every permissible N). For instance t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon where the quantum state of each Subatomic particle, particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurement#Quantum mechanics, Measurements of physical properties such as position (vector), position, momentum, Spin (physics), spin, and polarization (waves), polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Physics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Measurement
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region or another when an experiment is performed to locate it. This is the best the theory can do; it cannot say for certain where the electron will be found. The same quantum state can also be used to make a prediction of how the electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chaos
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of the Planck constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos (although this may not be a fruitful way of examining classical chaos). If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics? Michael Berry, "Quantum Chaology", pp 104-5 of ''Quantum: a guide for the perplexed'' by Jim Al-Khalili (Weidenfeld ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
