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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
e053809e1b3b7da9adb63abd9ab2cb36d8f3adc1	the problem of determining the adiabaticity of a	the problem of determining the adiabaticity of a given process is equivalent to establishing the dependence of u ^ (t 1, t 0) {\displaystyle {\hat {u}}(t_{1},t_{0})} on τ {\displaystyle \tau }.	wikipedia
0baf9210a026df4e3b6706206f79f9b2a4be1f50	along with the initial condition u ^ (t	along with the initial condition u ^ (t 0, t 0) = 1 {\displaystyle {\hat {u}}(t_{0},t_{0})=1}. given knowledge of the system wave function at t 0 {\displaystyle t_{0}}, the evolution of the system up to a later time t {\displaystyle t} can be obtained using	wikipedia
773b8982c3b407930a7fcfe33db92afd77c8c765	consider a system hamiltonian undergoing continuous change from	consider a system hamiltonian undergoing continuous change from an initial value h ^ 0 {\displaystyle {\hat {h}}_{0}}, at time t 0 {\displaystyle t_{0}}, to a final value h ^ 1 {\displaystyle {\hat {h}}_{1}}, at time t 1 {\displaystyle t_{1}}, where τ = t 1 − t 0 {\displaystyle \tau =t_{1}-t_{0}}. the evolution of the ...	wikipedia
74ad999cfa446568262a4bc11ef8f01d484afc60	often a solid crystal is modeled as a	often a solid crystal is modeled as a set of independent valence electrons moving in a mean perfectly periodic potential generated by a rigid lattice of ions. with the adiabatic theorem we can also include instead the motion of the valence electrons across the crystal and the thermal motion of the ions as in the born–o...	wikipedia
a134ae662c1fb0685dbc57407acd39548e7d9b81	in particular, \| c n (t) \| 2	in particular, \| c n (t) \| 2 = \| c n (0) \| 2 {\displaystyle \|c_{n}(t)\|^{2}=\|c_{n}(0)\|^{2}}, so if the system begins in an eigenstate of h (0) {\displaystyle h(0)}, it remains in an eigenstate of h (t) {\displaystyle h(t)} during the evolution with a change of phase only.	wikipedia
e305021e8c40789aad84e4120d8467c240f1f5a9	and geometric phase γ m (t) = i	and geometric phase γ m (t) = i ∫ 0 t ⟨ m (t ′) \| m ˙ (t ′) ⟩ d t ′. {\displaystyle \gamma _{m}(t)=i\int _{0}^{t}\langle m(t')\|{\dot {m}}(t')\rangle dt'.}	wikipedia
054ee35271ac3613ffc3ef5788c6e0bb49e2e730	with the dynamical phase θ m (t) =	with the dynamical phase θ m (t) = − 1 ℏ ∫ 0 t e m (t ′) d t ′ {\displaystyle \theta _{m}(t)=-{\frac {1}{\hbar }}\int _{0}^{t}e_{m}(t')dt'}	wikipedia
cca9c6399704350930f981350eef9b045b4fe14e	under a slowly changing hamiltonian h (t) {\displaystyle	under a slowly changing hamiltonian h (t) {\displaystyle h(t)} with instantaneous eigenstates \| n (t) ⟩ {\displaystyle \|n(t)\rangle } and corresponding energies e n (t) {\displaystyle e_{n}(t)}, a quantum system evolves from the initial state \| ψ (0) ⟩ = ∑ n c n (0) \| n (0) ⟩ {\displaystyle \|\psi (0)\rangle =\sum _{n}c...	wikipedia
9b718b1d17514e7bd1a3a39b3309695b14e62034	figure 2 shows the dependence of the diabatic	figure 2 shows the dependence of the diabatic and adiabatic energies on the value of the magnetic field; note that for non-zero coupling the eigenvalues of the hamiltonian cannot be degenerate, and thus we have an avoided crossing. if an atom is initially in state \| ϕ 2 (t 0) ⟩ {\displaystyle \|\phi _{2}(t_{0})\rangle }...	wikipedia
5e057f11ab3af8c4eeb7913f070a1f07c7d96f72	it is important to realise that the eigenvalues	it is important to realise that the eigenvalues ε 1 (t) {\displaystyle \varepsilon _{1}(t)} and ε 2 (t) {\displaystyle \varepsilon _{2}(t)} are the only allowed outputs for any individual measurement of the system energy, whereas the diabatic energies e 1 (t) {\displaystyle e_{1}(t)} and e 2 (t) {\displaystyle e_{2}(t)...	wikipedia
f36df6f94368dac75ff751427c4c629412778af6	the eigenvectors of the matrix h {\displaystyle \mathbf	the eigenvectors of the matrix h {\displaystyle \mathbf {h} } are the eigenstates of the system, which we will label \| ϕ 1 (t) ⟩ {\displaystyle \|\phi _{1}(t)\rangle } and \| ϕ 2 (t) ⟩ {\displaystyle \|\phi _{2}(t)\rangle }, with corresponding eigenvalues ε 1 (t) = − 1 2 4 a 2 + (ℏ ω 0 − 2 μ b (t)) 2 ε 2 (t) = + 1 2 4 a 2...	wikipedia
7961d8c4d9c4c54e4bade674ba00f7bbb4202b28	where μ {\displaystyle \mu } is the magnetic	where μ {\displaystyle \mu } is the magnetic moment of the atom, assumed to be the same for the two diabatic states, and a {\displaystyle a} is some time-independent coupling between the two states. the diagonal elements are the energies of the diabatic states (e 1 (t) {\displaystyle e_{1}(t)} and e 2 (t) {\displaystyl...	wikipedia
9a913580caa4f24ee0c4fa9b0ab4bd8b0c83b343	with the field absent, the energetic separation of	with the field absent, the energetic separation of the diabatic states is equal to ℏ ω 0 {\displaystyle \hbar \omega _{0}}; the energy of state \| 1 ⟩ {\displaystyle \|1\rangle } increases with increasing magnetic field (a low-field-seeking state), while the energy of state \| 2 ⟩ {\displaystyle \|2\rangle } decreases with...	wikipedia
bd245bf5c08f1edb9d8f70987f869cde236d65d9	for a more widely applicable example, consider a	for a more widely applicable example, consider a 2- level atom subjected to an external magnetic field. the states, labelled \| 1 ⟩ {\displaystyle \|1\rangle } and \| 2 ⟩ {\displaystyle \|2\rangle } using bra–ket notation, can be thought of as atomic angular-momentum states, each with a particular geometry. for reasons tha...	wikipedia
c9420f57c11162f3e711aed488fd81ff128effc4	for a rapidly increased spring constant, the system	for a rapidly increased spring constant, the system undergoes a diabatic process (d k d t → ∞) {\textstyle \left({\frac {dk}{dt}}\to \infty \right)} in which the system has no time to adapt its functional form to the changing conditions. while the final state must look identical to the initial state (\| ψ (t) \| 2 = \| ψ ...	wikipedia
4c585fbb6855c758e43f2515a3ca7d8b921f50d8	if k {\displaystyle k} is increased adiabatically (d	if k {\displaystyle k} is increased adiabatically (d k d t → 0) {\textstyle \left({\frac {dk}{dt}}\to 0\right)} then the system at time t {\displaystyle t} will be in an instantaneous eigenstate ψ (t) {\displaystyle \psi (t)} of the current hamiltonian h ^ (t) {\displaystyle {\hat {h}}(t)}, corresponding to the initial...	wikipedia
2ce76c195bfec0571118409be2464075a0ba4f2b	the classical nature of a pendulum precludes a	the classical nature of a pendulum precludes a full description of the effects of the adiabatic theorem. as a further example consider a quantum harmonic oscillator as the spring constant k {\displaystyle k} is increased. classically this is equivalent to increasing the stiffness of a spring; quantum-mechanically the e...	wikipedia
8d59c3307d520cae753952f5b505d09f2012d46f	as an example, consider a pendulum oscillating in	as an example, consider a pendulum oscillating in a vertical plane. if the support is moved, the mode of oscillation of the pendulum will change. if the support is moved sufficiently slowly, the motion of the pendulum relative to the support will remain unchanged. a gradual change in external conditions allows the syst...	wikipedia
cd503f83f0a03fdab604dfec260a50fe384abd1f	in the quantum world adiabatic means for example	in the quantum world adiabatic means for example that the time scale of electrons and photon interactions is much faster or almost instantaneous with respect to the average time scale of electrons and photon propagation. therefore, we can model the interactions as a piece of continuous propagation of electrons and phot...	wikipedia
4275a14b92a780c0761117faab864e8115e32465	the classical and quantum mechanics definition is instead	the classical and quantum mechanics definition is instead closer to the thermodynamical concept of a quasistatic process, which are processes that are almost always at equilibrium (i.e. that are slower than the internal energy exchange interactions time scales, namely a "normal" atmospheric heat wave is quasi-static, a...	wikipedia
56252fbafa1f307ac7e11719f070316ab16a3d47	the term "adiabatic" is traditionally used in thermodynamics	the term "adiabatic" is traditionally used in thermodynamics to describe processes without the exchange of heat between system and environment (see adiabatic process), more precisely these processes are usually faster than the timescale of heat exchange. (for example, a pressure wave is adiabatic with respect to a heat...	wikipedia
9502c6c3c214f05f0b27050697ef4920f586fd07	the so-called "gap condition" included in born and	the so-called "gap condition" included in born and fock's original definition given above refers to a requirement that the spectrum of h ^ {\displaystyle {\hat {h}}} is discrete and nondegenerate, such that there is no ambiguity in the ordering of the states (one can easily establish which eigenstate of h ^ (t 1) {\dis...	wikipedia
142a7e5538e023f058c37541dc3a52c7fd54cc3a	the degree to which a given change approximates	the degree to which a given change approximates an adiabatic process depends on both the energy separation between ψ (x, t 0) {\displaystyle \psi (x,t_{0})} and adjacent states, and the ratio of the interval τ {\displaystyle \tau } to the characteristic timescale of the evolution of ψ (x, t 0) {\displaystyle \psi (x,t_...	wikipedia
46b1e46a2d431a463c269304f170d12028547a9d	for a truly adiabatic process we require τ	for a truly adiabatic process we require τ → ∞ {\displaystyle \tau \to \infty }; in this case the final state ψ (x, t 1) {\displaystyle \psi (x,t_{1})} will be an eigenstate of the final hamiltonian h ^ (t 1) {\displaystyle {\hat {h}}(t_{1})}, with a modified configuration:	wikipedia
c7c8e100a8359a990889ef730cce93d09e4551c9	at some initial time t 0 {\displaystyle t_{0}}	at some initial time t 0 {\displaystyle t_{0}} a quantum-mechanical system has an energy given by the hamiltonian h ^ (t 0) {\displaystyle {\hat {h}}(t_{0})}; the system is in an eigenstate of h ^ (t 0) {\displaystyle {\hat {h}}(t_{0})} labelled ψ (x, t 0) {\displaystyle \psi (x,t_{0})}. changing conditions modify the ...	wikipedia
4ec9ae96852861d1c5da54a3ffba14bff501e3ec	at the 1911 solvay conference, einstein gave a	at the 1911 solvay conference, einstein gave a lecture on the quantum hypothesis, which states that e = n h ν {\displaystyle e=nh\nu } for atomic oscillators. after einstein's lecture, hendrik lorentz commented that, classically, if a simple pendulum is shortened by holding the wire between two fingers and sliding down...	wikipedia
f60f1455e1fbdaabb984a6352549899d544ab292	reid philip simpson is a canadian former professional	reid philip simpson is a canadian former professional ice hockey left winger who played twelve seasons in the national hockey league (nhl) for the philadelphia flyers, minnesota north stars, new jersey devils, chicago blackhawks, tampa bay lightning, st. louis blues, montreal canadiens, nashville predators and pittsbur...	wikipedia
ea8654467b9c721e76069827b78c3647fbeb1cbe	simpson was drafted 72nd overall by the flyers	simpson was drafted 72nd overall by the flyers in the 1989 nhl entry draft and went on to play in 301 regular season games, notching up 18 goals and 18 assists for 36 points, racking up 838 penalty minutes in the process. he won a calder cup with the albany river rats in 1995. the veteran attempted a comeback during th...	wikipedia
ad9441da4021f7face690d65b60aabf0054bebfe	reid philip simpson (born may 21, 1969) is	reid philip simpson (born may 21, 1969) is a canadian former professional ice hockey left winger who played twelve seasons in the national hockey league (nhl) for the philadelphia flyers, minnesota north stars, new jersey devils, chicago blackhawks, tampa bay lightning, st. louis blues, montreal canadiens, nashville pr...	wikipedia
617174425792240f41b102195edf9424dd84cd88	silpheed is a video game developed by game	silpheed is a video game developed by game arts and designed by takeshi miyaji. it made its debut on the japanese pc-8801 in 1986, and was ported to the fujitsu fm-7 and dos formats soon after. it was later remade for the sega cd and has a sequel called silpheed: the lost planet for the playstation 2. silpheed is the n...	wikipedia
003740c7c815998a317fd577e956331891d8945b	mega placed the game at #5 in their	mega placed the game at #5 in their top mega-cd games of all time, megatech magazine said the game was "undoubtedly one of the best games yet for the mega-cd". this version of the game was a bestseller in japan. the sega cd version was a runner-up for gamepro ' s 1993 cd game of the year award.	wikipedia
1c425cac158ce89c57177246dbc48e273a899f08	the four reviewers of electronic gaming monthly gave	the four reviewers of electronic gaming monthly gave the sega cd version scores of 9, 7, 7 and 7 out of 10. they said it is a "rather mundane" and "simple shooter" but the "game play is solid" and the backgrounds are "some of the most stunning visuals in a video game". however, they criticized the unimpressive bosses, ...	wikipedia
808e55f754e17feaf155c606d14d9ca565fdad67	in 1989, dragon gave the dos version of	in 1989, dragon gave the dos version of the game 5 out of 5 stars, concluding that " silpheed is highly addictive, extremely colorful, and requires hours of enjoyable practice to master". computer gaming world gave the same version a positive review, praising the original music for the game. the british gaming magazine...	wikipedia
f7d191410b84b157f1e61ff2ea4ff6cab7519374	the game's story concerns a space war campaign	the game's story concerns a space war campaign when terrorists—led by a man named xacalite—hack into the mother computer of earth, granting them control over all the space weaponry of the solar system. the earth's only hope is a small fleet outside the computer's reach, provided with a squadron of sa-77 silpheed dogfig...	wikipedia
4939df85469dd6c46324f960f51052eae0fee984	the sega cd port of silpheed places polygon	the sega cd port of silpheed places polygon ships over a pre-rendered video background; this method is also seen in other video game titles, such as namco's galaxian 3 in 1990 and starblade in 1991, sony imagesoft 's bram stoker's dracula in 1992, and micronet's a/x-101 in 1994 for the sega cd.	wikipedia
c7894a38b2d6355f6b3c20466c12cb7470a880e1	the storyline is that in the future (no	the storyline is that in the future (no date is specified, though 3032 is referred to as the date when an alien ship was discovered that led to rapid technological advancement and allowed humans to colonize outer space) a terrorist named xacalite has stolen "planetary buster" missiles and a battleship named gloire. the...	wikipedia
6f4095f32c7d087439ba06a48df5ae03dcc90394	in 1989 sierra on-line also ported silpheeed to	in 1989 sierra on-line also ported silpheeed to the apple iigs, which supported the same 640x200 graphics modes of the original nec pc-8801 version, and its full musical score (based on the roland mt-32 soundtrack from the dos version) using its 15-voice ensoniq sound chip.	wikipedia
63e0bb959fea96fccf18068d94fdc5d37246a921	the original silpheed game was created for the	the original silpheed game was created for the pc-8801, and released on december 5, 1986. another version for the fm-7 was released on march 3, 1988. in the same year, the game was brought to the united states for the first time by sierra on-line who ported the game to dos and other platforms. the dos version (1.0) rel...	wikipedia
ef225509b91dec440d8c778596df8fb3edd48489	silpheed is a vertical-scrolling shooter video game. it	silpheed is a vertical-scrolling shooter video game. it is presented at an oblique view camera angle, with enemies and other objects becoming smaller as they move towards the top of the screen. the player assumes the role of a starship named the sa-08 silpheed, deployed by the yggdrassil supercomputer to destroy the xa...	wikipedia
e831e7e8700adce82014d51b5d0e7fe4726e01dd	silpheed is the name of the spacecraft that	silpheed is the name of the spacecraft that the player controls, and is most likely derived from the famous ballet, la sylphide. like many shooter games, the story involves using the silpheed as earth's last effort to save itself from destruction by a powerful enemy invasion. the original 1986 pc-88 version used 3d pol...	wikipedia