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- ...3 = Latha Gearheart }}</ref> [[File:Quantum Dots.jpg|thumb|'''Figure 1:''' Quantum dot solutions emitting yellow-orange and light-blue light, excited by UV li ...or [[biocompatibility]], in addition to the development of Cd-free quantum dots ("CFQDs"). After a [[surface modification]] has been made to limit [[toxici ...18 KB (2,573 words) - 01:12, 10 June 2024
- ...in which they form an extended [[hydrogel]] network. In this form, quantum dots can be utilized in several applications that benefit from their unique prop == Quantum dots == ...18 KB (2,526 words) - 22:13, 3 February 2024
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- ...''<sub>h</sub>*. <ref>{{Cite book |last=Linke |first=Heiner |title=Quantum dots – Seeds of Nanoscience |publisher=The Royal Swedish Academy of Sciences |ye ...is the [[speed of light]]). This is useful for calculating the radius of a quantum dot from experimentally determined parameters. ...2 KB (356 words) - 13:06, 14 October 2024
- ...)\in \mathbb{N}^r</math> and <math>r</math> positive measures <math>\mu_1,\dots,\mu_r</math> over the reals. As usual <math>|\vec{n}|:=n_1+n_2+\cdots + n_r Polynomials <math>A_{\vec{n},j}</math> for <math>j=1,2,\dots,r</math> are of ''type 1'' if the <math>j</math>-th polynomial <math>A_{\ve ...3 KB (499 words) - 12:59, 27 June 2023
- *The quantum plane, the most basic example, is the [[quotient ring]] of the free ring: *More generally, the '''quantum polynomial ring''' is the quotient ring: ...2 KB (245 words) - 08:59, 28 August 2021
- ...th. [https://dx.doi.org/10.1007/BF00739578 The Bogoliubov inner product in quantum statistics], ''Letters in Mathematical Physics'' '''27''', 205-216 (1993).< ...ath>H</math> is the [[Hamiltonian (quantum mechanics)|Hamiltonian]] of the quantum system and <math>\beta </math> is the [[inverse temperature]]. With these n ...2 KB (383 words) - 18:26, 25 February 2022
- ...omputer|quantum]] benchmarking protocol which can be used to demonstrate [[quantum supremacy]].<ref>{{Cite journal |title = Characterizing Quantum Supremacy in Near-Term Devices ...4 KB (522 words) - 19:33, 10 December 2024
- ...n]] <math>\psi(x_1, x_2, \dots, x_j, \dots,x_N)</math>. The [[Hamiltonian (quantum mechanics)|Hamiltonian]], of this model is introduced as ....com/books?id=g0KjDwAAQBAJ&dq=lieb+liniger+model&pg=PA549 |title=Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz |date=2019-07- ...5 KB (888 words) - 17:13, 13 February 2025
- ...973).</ref> Mark Fannes is a Belgian physicist specialised in mathematical quantum mechanics, and he works at the [[Katholieke Universiteit Leuven|KU Leuven]] :<math>\rho = \mathrm{Diag}(1-T, T/(d-1),\dots,T/(d-1)) </math> ...4 KB (569 words) - 10:05, 29 August 2024
- ...=126244962 }}</ref> is the expansion of different scattering quantities in quantum scattering theory in the powers of the interaction potential <math> V </mat ...V |\phi\rangle + [G_0(E) V]^2 |\phi\rangle + [G_0(E) V]^3 |\phi\rangle + \dots </math> ...4 KB (660 words) - 09:11, 17 December 2022
- | known_for = {{ublist|[[Quantum computing]]|[[Loss–DiVincenzo quantum computer]]| [[DiVincenzo's criteria]]}} .../spectrum.ieee.org/david-divincenzo-on-his-tenure-at-ibm-and-the-future-of-quantum-computing |date=2 October 2015 |work=[[IEEE Spectrum]] |access-date=14 Dece ...6 KB (771 words) - 04:24, 31 July 2024
- .... an ordered basis <math>({\mathbf e}_1,\dots,{\mathbf e}_n,{\mathbf f}_1,\dots,{\mathbf f}_n)\,</math> of tangent vectors at <math>p\,</math> of the tange for <math>j,k=1,\dots,n\,</math>. For <math>p\in M\,</math>, each fiber <math>{\mathbf R}_p\,</ma ...2 KB (374 words) - 01:54, 29 April 2024
- {{Short description|Family of quantum invariants}} ...''Reshetikhin–Turaev invariants''' ('''RT-invariants''') are a family of [[quantum invariants]] of [[framed link]]s. ...9 KB (1,517 words) - 19:13, 9 October 2024
- Given a sequence of tensors <math>T_1, T_2, \dots, T_n</math>, the tensotory is defined as the iterated tensor product: \bigotimes_{i=1}^n T_i = T_1 \otimes T_2 \otimes \dots \otimes T_n ...4 KB (635 words) - 01:52, 9 January 2025
- ...com/books?id=0BMpCwAAQBAJ&dq=meir-wingreen-jauho&pg=PA216 |title=Theory of Quantum Transport at Nanoscale: An Introduction |date=2015-12-08 |publisher=Springe ...lating the current through various systems, such as molecular junctions, [[quantum dot]]s and [[nanoscale device]]s. ...3 KB (408 words) - 23:58, 14 February 2025
- {{Short description|Quantum algorithm}} [[File:Bernstein-Vazirani quantum circuit.png|thumb]] ...7 KB (1,097 words) - 20:26, 20 February 2025
- ...3 = Latha Gearheart }}</ref> [[File:Quantum Dots.jpg|thumb|'''Figure 1:''' Quantum dot solutions emitting yellow-orange and light-blue light, excited by UV li ...or [[biocompatibility]], in addition to the development of Cd-free quantum dots ("CFQDs"). After a [[surface modification]] has been made to limit [[toxici ...18 KB (2,573 words) - 01:12, 10 June 2024
- ...ion and computation, it is essential to construct coherent combinations of quantum states. ...ions can be performed on a sequence of pairs of physically distinguishable quantum bits and, therefore, can be illustrated by a simple four-level system. ...13 KB (1,886 words) - 09:12, 13 September 2024
- ...MT remained elusive. After Garoufalidis–Lê–Zeilberger's [[Quantum algebra|quantum]] extension (2006), a number of [[Noncommutative geometry|noncommutative]] G(k_1,\dots,k_m) \, = \, \bigl[x_1^{k_1}\cdots x_m^{k_m}\bigr] \, ...9 KB (1,258 words) - 02:17, 11 February 2023
- The '''Wannier equation''' describes a quantum mechanical [[Eigenvalues and eigenvectors|eigenvalue problem]] in [[solids] ...th> and eigenenergy <math>E_\lambda</math> where <math>\lambda</math> is a quantum number labeling the different states. ...10 KB (1,441 words) - 09:03, 11 October 2023
- {{Short description|Generalization of laser spectroscopy in quantum optics}} '''Quantum-optical spectroscopy'''<ref name="KiraKoch2006">Kira, M.; Koch, S. (2006). ...17 KB (2,209 words) - 15:41, 26 July 2022
- [[File:Quantum ergodicity.gif|thumb|360px|right|The eigenmode of a classically integrable ...y|chaotic]] in the sense of exponential sensitivity to initial conditions. Quantum ergodicity states, roughly, that in the high-energy limit, the probability ...11 KB (1,546 words) - 09:50, 31 May 2024