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40749152443
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The confining potential V(x)=I V0x (2kx nπ) 2 continues the periodic potential at "x"= x0, where n is the number of sites. The potential is continuously differentiable which determines I (1) and x0 (naa 2).
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The confining potential V(x)=I V0x (2kx nπ) 2 continues the periodic potential at "x"= x0, where n is the number of sites. The potential is continuously differentiable which determines I (1) and x0 (naa 2).
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40749139590
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We used up to 100 000 basis states and parity conservation if applicable including the formed Bloch bands and the lowest “continuuma states (bound states in the confinement).
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We used up to 100 000 basis states and parity conservation if applicable including the formed Bloch bands and the lowest “continuuma states (bound states in the confinement).
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40749109518
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The first excited state 1 ="1, 1= bs basa "0 remains unchanged and the second excited state is given by 2 =cos I"2,0 +sin "0,2=atan[(I+I 2 + I2) I].
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The first excited state 1 ="1, 1= bs basa "0 remains unchanged and the second excited state is given by 2 =cos I"2,0 +sin "0,2=atan[(I+I 2 + I2) I].
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We can confirm the experimental observation and the calculation in Ref. also by the diagonalization of several bosons on a single site. The on-site energy U of filling factor I=5 is, e.g., roughly 17% smaller than for I =1 at V0 =30 ER.
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We can confirm the experimental observation and the calculation in Ref. also by the diagonalization of several bosons on a single site. The on-site energy U of filling factor I =5 is, e.g., roughly 17% smaller than for I =1 at V0 =30 ER.
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40749151622
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The density on one site corresponds to the density of a single particle in a single-sited cos2 potential, but deviates slightly from the harmonic approach.
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The density on one site corresponds to the density of a single particle in a single-sited cos2 potential, but deviates slightly from the harmonic approach.
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40749105438
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Additional information can be obtained from the pair correlation function G2 (x, x) in deep lattices with one particle fixed in the middle of a specific site. As seen before, the correlation vanishes at that site for filling factor I =1. For noninteger filling (6N 9) the height of the correlation function varies for each site. Thus, regarding the integer number of particles, at least some particles must be delocalized between the sites.
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Additional information can be obtained from the pair correlation function G2 (x, x) in deep lattices with one particle fixed in the middle of a specific site. As seen before, the correlation vanishes at that site for filling factor I =1. For noninteger filling (6N 9) the height of the correlation function varies for each site. Thus, regarding the integer number of particles, at least some particles must be delocalized between the sites.
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The first and second excited state, the third and fourth excited state as well as the sixth and seventh excited state are exactly degenerate.
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The first and second excited state, the third and fourth excited state as well as the sixth and seventh excited state are exactly degenerate.
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