The effect of disorder is one of the most interesting and ubiquitous problems in condensed matter physics. A fundamental question, "How does a ground state evolve in response to increasing disorder?", encompasses many areas in modern condensed matter physics, especially in conjunction with quantum phase transitions. We address the same question in the low temperature phases of liquid 3He, which is of a special interest since, in its bulk form, it is the most well understood unconventional superfluid and the purest substance known to mankind. Unlike conventional s-wave pairing superconductors, the unconventional superconductors are vulnerable to any type of impurity, and this fact has been used to test the unconventional nature of the order parameter in heavy fermion and cuprate superconductors. The aerogel/3He system provides a unique opportunity to conduct a systematic investigation on the effects of static disorder in unconventional superfluids. We have investigated the influence of disorder, introduced in the form of 98% porosity silica aerogel, on the superfluid 3He using various ultrasound techniques. Our primary effort is in understanding the complete phase diagram of this relatively new system. In particular, the high magnetic field region of the phase diagram has not been explored until this work, and the nature of the A-like to B-like transition in this system has not been elucidated. We identified a third superfluid phase emerging in the presence of magnetic fields, which resembles, in many respects, the A1-phase in bulk. Our zero field study of the A-B transition in aerogel revealed that two phases coexist in a narrow window of temperature right below the superfluid transition. Sound attenuation measurements conducted over a wide range of temperatures and pressures show a drastically different behavior than in bulk. In particular, in the B-like phase, our results can be interpreted as strong evidence of a gapless superfluid.
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