Science desk | ||
---|---|---|
< June 13 | << May | June | Jul >> | June 15 > |
Welcome to the Wikipedia Science Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
To start off, consider the simplest quantum system: a two-dimensional Hilbert space, or "qubit". The classical states are the 0 and the 1. If the system is isolated, then there exists a unitary time evolution operator which can be represented as a 2x2 matrix, e.g.
which acts on and and linear combinations thereof. The state of the system after n time steps is found by applying to the initial state.
For example, , and subsequently the probability of observing the system in the 0 state is .
When the system is "open", the operator U "keeps track of the history". Denote the history of a state as a sequence of 0s and 1s, for example, is a sequence whose most recent state is the 0 state. Denote the new operator .
Now, for instance, , and .
The difference is that and , although both representing the 0 state, have different histories and therefore the probability of observing the system in the 0 state is now .
It can be shown that as you take , the probability of observing the qubit in the 0 state (the sum of norm-squared probability amplitudes of all sequences whose most recent element is the 0 state) converges on .
In fact, for a quantum system described by an m-dimensional Hilbert space, it can be shown that the probability of observing the system in any given state approaches --all states are equiprobable in the long run.
What I want to know is what happens when the quantum system is described by an infinite-dimensional Hilbert space, such as a quantum field. Is the long run probability distribution of states still uniform in that case? My guess is that the answer is no, but that there is a long run equilibrium which is different from the uniform distribution over possible states.-- 49.183.144.209 ( talk) 11:57, 14 June 2019 (UTC)
Is it bad to weight lift 2 days in a row? A lot of professional weight lifters like Bruce Lee do a Mon/Wed/Fri schedule or Tu/Th/Sat schedule. The logic is that muscles need 48 hours to heal. But what is the argument against weight lifting 2 days in a row? Because I also hear, weight lifting just makes muscle cells bigger, bu if you want new muscle cells to be created, you need to lift when you're sore, so that could be M/T and Th/Fr schedule. Shrug. 67.175.224.138 ( talk) 15:41, 14 June 2019 (UTC).
I stayed in a dorm when I went to university and each room had two desk areas, each with a desk lamp attached to the wall by way of an articulated arm. The bulbs were incandescent (this was in the 90s). Someone had heard of a neat trick involving such set ups, which turned out to be true. If you smack the shade of the light hard enough so that the entire system is shocked, the bulb will burn brighter - quite a bit brighter actually. None of us had access to a light meter, but I'd bet they were easily twice as bright. Unsurprisingly, some of the bulbs died shortly afterwards (I'll say, over the course of the next week or two), while others kept working fine for the rest of the semester. For whatever reason, that "experiment" recently came to my mind. What the heck was actually happening? I described the set up as best I can recall, in case that had something to do with it, but I presume the effect was caused by shocking the bulb itself...? When it gets right down to it, none of it makes much sense, but we - ahem - conducted several iterations of the test, almost all of which worked. Matt Deres ( talk) 22:31, 14 June 2019 (UTC)
Science desk | ||
---|---|---|
< June 13 | << May | June | Jul >> | June 15 > |
Welcome to the Wikipedia Science Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
To start off, consider the simplest quantum system: a two-dimensional Hilbert space, or "qubit". The classical states are the 0 and the 1. If the system is isolated, then there exists a unitary time evolution operator which can be represented as a 2x2 matrix, e.g.
which acts on and and linear combinations thereof. The state of the system after n time steps is found by applying to the initial state.
For example, , and subsequently the probability of observing the system in the 0 state is .
When the system is "open", the operator U "keeps track of the history". Denote the history of a state as a sequence of 0s and 1s, for example, is a sequence whose most recent state is the 0 state. Denote the new operator .
Now, for instance, , and .
The difference is that and , although both representing the 0 state, have different histories and therefore the probability of observing the system in the 0 state is now .
It can be shown that as you take , the probability of observing the qubit in the 0 state (the sum of norm-squared probability amplitudes of all sequences whose most recent element is the 0 state) converges on .
In fact, for a quantum system described by an m-dimensional Hilbert space, it can be shown that the probability of observing the system in any given state approaches --all states are equiprobable in the long run.
What I want to know is what happens when the quantum system is described by an infinite-dimensional Hilbert space, such as a quantum field. Is the long run probability distribution of states still uniform in that case? My guess is that the answer is no, but that there is a long run equilibrium which is different from the uniform distribution over possible states.-- 49.183.144.209 ( talk) 11:57, 14 June 2019 (UTC)
Is it bad to weight lift 2 days in a row? A lot of professional weight lifters like Bruce Lee do a Mon/Wed/Fri schedule or Tu/Th/Sat schedule. The logic is that muscles need 48 hours to heal. But what is the argument against weight lifting 2 days in a row? Because I also hear, weight lifting just makes muscle cells bigger, bu if you want new muscle cells to be created, you need to lift when you're sore, so that could be M/T and Th/Fr schedule. Shrug. 67.175.224.138 ( talk) 15:41, 14 June 2019 (UTC).
I stayed in a dorm when I went to university and each room had two desk areas, each with a desk lamp attached to the wall by way of an articulated arm. The bulbs were incandescent (this was in the 90s). Someone had heard of a neat trick involving such set ups, which turned out to be true. If you smack the shade of the light hard enough so that the entire system is shocked, the bulb will burn brighter - quite a bit brighter actually. None of us had access to a light meter, but I'd bet they were easily twice as bright. Unsurprisingly, some of the bulbs died shortly afterwards (I'll say, over the course of the next week or two), while others kept working fine for the rest of the semester. For whatever reason, that "experiment" recently came to my mind. What the heck was actually happening? I described the set up as best I can recall, in case that had something to do with it, but I presume the effect was caused by shocking the bulb itself...? When it gets right down to it, none of it makes much sense, but we - ahem - conducted several iterations of the test, almost all of which worked. Matt Deres ( talk) 22:31, 14 June 2019 (UTC)